/Tsironomical 


UC-NRLF 


PRIVATE    LIBRARY 
OF 

CHARLES  A.  KOFOID. 

Cost..«U>. 


THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 

PRESENTED  BY 

PROF.  CHARLES  A.  KOFOID  AND 
MRS.  PRUDENCE  W.  KOFOID 


THE  EARTH  IN  SPACE 


Manual  of 


ASTRONOMICAL  GEOGRAPHY 


BY 


EDWARD  P.  JACKSON,  A.M. 

INSTRUCTOR  IN  PHYSICAL  SCIENCE  IN  THE  BOSTON  LATIN  SCHOOL 


BOSTON 

D.  C.   HEATH  &  CO.,  PUBLISHERS 
1889 


COPYRIGHT,  1887. 
BY  EDWARD  P.  JACKSON. 


TYPOGRAPHY  BY  J.  S.  GUSHING  &  Co. 


PRESSWORK  BY  BERWICK  &  SMITH,  BOSTON. 


66 


PREFACE. 


THIS  little  manual  is  a  condensed  and  simplified  ver- 
sion of  a  Mathematical  Geography  published  several 
years  ago.  It  has  been  prepared  in  compliance  with 
the  request  of  the  late  Miss  Lucretia  Crocker,  a  super- 
visor of  the  Boston  Public  Schools,  and  of  many  other 
advocates  of  more  thorough  instruction  in  this  branch. 

It  is  designed  for  Grammar  Schools,  and  for  High  and 
Normal  Schools  where  Astronomy  is  not  prescribed,  but 
where  an  hour  a  day  for  a  few  days  can  be  spared  for  this 
most  practical  department  of  Astronomy. 

The  proofs  have  been  read  by  Dr.  J.  R.  Webster,  Mr. 
C.  F.  King,  and  others.  At  the  suggestion  of  several  of 
these  readers,  certain  passages  which  may  be  found  too 
difficult  for  Grammar-School  classes  are  marked  with  the 
character  (f).  The  substance  of  these  passages  may  be 
given  orally  by  the  teacher,  or,  if  necessary,  they  may  be 
omitted  altogether. 

Those  wishing  a  fuller  presentation  of  the  more  diffi- 
cult topics  are  referred  to  the  larger  work  mentioned 
above. 


M34S189 


CONTENTS. 


PAGE 

I.    SPHERICAL  FORM  OF  THE  EARTH i 

How  we  know  that  the  Earth  is  Spherical      ...  2 

II.    DEPARTURES  FROM  THE  SPHERICAL  FORM    ...  5 
How  we  know  that  the  Earth  is  flattened  at  the 

Poles 7 

III.  LATITUDE  AND  LONGITUDE 9 

IV.  ZONES 13 

The  Zones  are  Natural  Divisions 14 

V.    DIMENSIONS  AND  DISTANCES 16 

How  we  know  the  Magnitudes,  etc.,  of  the  Earth 

and  the  Other  Heavenly  Bodies 16 

VI.    THE  SUN'S  RAYS  AND  THE  EARTH'S  ATMOSPHERE,  21 
Gradual  Changes  in  Light  and  Heat  during  the  Day 

and  the  Year 24 

VII.    THE  EARTH'S  DAILY  MOTION 28 

How  we  know  that  the  Earth  rotates 31 

Apparent  Daily  Motion  of  the  Heavens     ....  32 

VIII.    THE  EARTH'S  YEARLY  MOTION 39 

How  we  know  that  the  Earth  revolves  around  the 

Sun 42 

IX.    THE  INCLINATION  OF  THE  EARTH'S  Axis     ...  50 

The  Sun's  Declinations 54 

The  Change   of  Seasons.     The  Variation   in   the 

Length  of  Day  and  Night 57 

Additional  Observations 63 


APPENDIX 69 


THE   EARTH   IN   SPACE. 


I.  SPHERICAL  FORM  OF  THE  EARTH. 

IF  you  were  on  board  a  steamer  in  the  midst  of  the 
Atlantic  Ocean,  you  would  not  be  content  with  know- 
ing all  about  your  fellow-passengers,  the  internal  struc- 
ture of  the  vessel,  its  freight,  etc. ;  you  would  be  at 
least  equally  anxious  to  know  where  you  were  sailing, 
and  what  countries  and  other  objects  you  would  pass 
in  your  course. 

1.  The  Earth  is  a  Great  Spherical  Ship,  carrying 
you  swiftly  onward  in  the  ocean  of  space.     You  are 
now  asked  to  look  abroad  and  see  how,  why,  and 
where  you  are  moving,  and  what  objects  you  are  pass- 
ing at  greater  or  less  distances. 

2.  What  made  the  Earth  Spherical?  —  The  same 
cause    that   makes    the   raindrop   spherical,   viz.,    the 
mutual  attraction  of  its  particles.     Every  particle  of 
matter   in   the  universe   attracts,  or  tries  to  draw  to 
itself,  every  other  particle.     This  universal  attraction 
is  called  the  attraction  of  gravitation,  or  simply  gravi- 
tation. 

3.  How  Attraction  makes  the  Raindrop  Spherical. 
—  Every  one  knows  that  drops  of  rain  are  produced 


2  SPHERICAL   FORM   OF  THE  EARTH. 

by  invisible  particles  of  cloud  or  vapor  running  to- 
gether. We  may  imagine  two  or  three  of  these  parti- 
cles collecting  and  forming  a  little  body,  which  attracts 
more  powerfully  than  the  single  particles  around  it.* 
We  may  then  imagine  the  surrounding  particles  gath- 
ering around  this  body  as  a  centre,  until  it  becomes 
heavy  enough  to  fall  as  a  drop  of  rain.  Now,  the  par- 
ticles in  the  drop  endeavor  to  approach  as  near  as 
possible  to  the  centre,  and  thus  form  a  sphere,  just  as 
a  party  of  men,  in  crowding  around  an  object,  form  a 
circle. 

4.  How  Gravitation  made  the  Earth  and  Other 
Heavenly  Bodies  Spherical.  —  In  precisely  the  same 
way.     We  may  imagine  a  time  when  the  particles  of 
matter   which    they  contain   were    scattered   through 
space,  like  particles  of  vapor  in  the  air,  and  we  may 
imagine    those    particles    collecting    around    different 
centres,  called  centres  of  gravitation,  until  spherical 
masses  were  formed  of  all  sizes,  from  that  of  the  rain- 
drop to  that  of  the  sun  itself. 

HOW  WE   KNOW  THAT  THE    EARTH    IS    SPHERICAL. 

5.  First  Proof. — The  curvature  of  its  surface  may  be 
actually  seen.     When  we  look  at  a  distant  object  upon 
the  ocean  or  across  a  wide  plain,  we  can  see  the  inter- 
vening surface  rounding  up  so  as  to  conceal  entirely 
the  lower  part  of  the  object.     This  convexity  is  always 
found  to  be  the  same  for  the  same  distance,  which 
could  not  be  the  case  except  upon  a  spherical  body. 

*  The  more  matter  a  body  contains,  the  more  powerfully  it  attracts. 


SPHERICAL   FORM  OF  THE  EARTH.  3 

Whenever  you  are  at  the  seaside  near  a  great  port,  you 
may  see  this  very  satisfactorily  illustrated :  the  more 
distant  vessels  are,  the  lower  they  seem  to  sink  behind 
the  convex  surface  of  the  water. 


i.    The  Curvature  of  the  Earth. 


A  more  accurate  experiment  consists  in  fixing  three 
targets  of  equal  height  at  equal  distances  upon  a  plain 
—  as  a  long  sea-beach — and  "sighting"  the  elevation 
of  the  middle  target  above  a  perfectly  straight  line 
connecting  the  other  two.  The  elevation  is  invariably 
found  to  be  the  same  for  equal  distances. 

6.  Second  Proof. —  Circumnavigation.    Navigators 
have  started  from  a  certain  point  and  sailed  constantly 
in  the  same  general  direction  until  they  have  finally 
reached  the  very  place  from  which  they  started.    Now, 
if  the  earth  were  of  any  other  form  than  round,  or  if 
there  were   great   edges   or   sudden   turnings  of  any 
description  in  its  form,  these  men  could  not  have  failed 
to  discover  indications  of  them. 

7.  Third  Proof.  —  The  Horizon    seems  both  to 
enlarge  and  to  sink  as  we  ascend  above  the  surface  ; 
whereas,  if  the  earth  were  an  extended  plain,  our  field 
of  view  would  not  change,  whatever  our  elevation.   The 
horizon  is  also  always  circular,  which  would  not  be  the 
case  if  the  earth's  form  differed  very  much  from  that 
of  a  sphere. 


4  SPHERICAL   FORM   OF  THE  EARTH. 

You  may  illustrate  this  readily  as  follows  :  Cut  a 
small  circular  hole  in  a  card,  and  place  it  upon  differ- 
ent parts  of  a  globe.  Supposing  an  observer  to  stand 
in  the  very  centre  of  the  aperture,  in  each  position, 
the  circle  around  him  represents  his  horizon.  If  some 
other  object  be  taken  to  represent  the  earth,  as  a  cube 
or  a  cylinder,  it  will  be  seen  that  the  hole  in  the  card 
must  be  of  different  forms  in  order  to  fit  different  parts 
of  its  surface.  That  part  of  the  globe  which  is  seen 
through  the  aperture  in  the  card  is  so  small  as  to 
appear  perfectly  flat.  This  explains  why  the  surfaces 
of  plains  and  of  the  ocean  seem  flat  to  the  ordinary 
observer. 

It  may  be  thought  that  the  three  proofs  given  above 
do  not  show  positively  that  the  earth  is  spherical  — 
that  it  might  be  of  some  other  rounding  form,  like  that 
of  an  egg,  for  example,  without  materially  affecting  the 
appearances  described.  Such  a  supposition  is  shown 
to  be  incorrect  from  the  two  proofs  which  follow. 

8.  Fourth  Proof.  —  The  Weight  of  a  Body  is  very 
nearly  the   same  at  all  parts  of  the  earth's  surface, 
which   could  not  be  the  case  if  the  earth  were  not 
nearly  spherical,  since  the  same  body  grows  heavier, 
the  nearer  it  approaches  (on  the  surface)  to  the  centre 
of  the  earth. 

9.  Fifth  Proof.  —  Eclipses.     In  the  course  of  the 
revolutions  of  the  heavenly  bodies,  the  earth  sometimes 
passes  exactly  between  the  sun  and  the  moon,  casting 
a  shadow  on  the  latter.     This  shadow  is  always  circu- 
lar, showing  that  the  earth  is  round  in  every  direction. 
If  it  were  round  in  only  one  direction,  like  a  coin  or  a 


DEPARTURES  FROM  THE  SPHERICAL  FORM.    *> 

medal,  its  shadow  would  be  circular  only  when  its  flat 
surface  exactly  faced  the  moon.  In  all  other  positions, 
the  shadow  would  vary  from  a  straight  line  to  an  oval 
of  different  degrees  of  breadth,  as  may  be  easily  proved 
by  experiment. 

10.  Up  and  Down.  —  These  directions  are  not  fixed 
in  space,  like  north  and  south,  but  depend  entirely 
upon  the  position  of  the  observer ;  and  since  the  earth 
is  a  sphere  with  observers  upon  all  sides  of  it,  up  may 
be  any  direction  from  the  centre  of  the  earth,  and 
down,  any  direction  towards  the  centre.  Apart  from 
the  earth  or  any  other  heavenly  body,  that  is,  in  space, 
there  are  no  such  directions  as  up  and  down. 


II.  DEPARTURES  FROM  THE  SPHERICAL 
FORM. 

11.  The  Earth's  Form  differs  from  that  of   a 
Perfect  Sphere  in  Two  Respects:  — 

(1)  Its  surface  is  uneven. 

(2)  It  is  flattened  at  the  poles.* 

12.  The  Amount  of  these  Departures  is  so  slight 
tnat,  if  the  whole  figure  of  the  earth  could  be  seen  at 
once,  as  by  a  spectator  upon  the  moon,  it  would  appear 
perfectly  round,  like  the  moon. 

13.  Unevenness  of  the  Surface.  —  In  order  to  be 
a  perfect  sphere,  the  earth's  surface  should  be   per- 

*  Careful  measurements  have  recently  shown  that  the  equator 
also  is  very  slightly  flattened  upon  two  opposite  sides. 


6    DEPARTURES  FROM  THE  SPHERICAL  FORM. 

fectly  smooth ;  for  hills  and  plains  are  not  "  equally 
distant  from  the  centre."*  Yet  there  are  still  higher 
mountains  and  deeper  valleys  on  the  moon,  which, 
nevertheless,  always  appears  to  us  perfectly  round.  All 
the  hills,  mountains,  valleys,  forests,  cities,  etc.,  on  the 
earth  are  so  extremely  small,  compared  with  its  own 
vast  bulk,  that  they  merely  serve  to  roughen  its  surface 
in  a  slight  degree. 

14.  The  Principal  Cause  of  the  Unevenness.  —  The 
earth  was  formerly  a  mass  of  melted  matter.     As  the 
outer  portions  cooled,  they  hardened  into  a  shell  of 
solid  rock,  called  the  crust.   This,  in  hardening,  shrunk, 
and   thus    formed   mountains   and  valleys,  just   as   a 
smooth  apple  becomes  puckered  when  it  dries  and  con- 
tracts.    Since  then,  volcanic  action,  which  is  nothing 
more  than  the  boiling  of  the  melted  matter  within  the 
crust,  has  modified  the  form  to  some  extent. 

15.  The  Flattening  at  the  Poles   is  due  to  the 

earth's  rotation,  which  has 
caused  those  parts  near  the 
equator  to  bulge  out,  and  those 
near  the  poles  to  sink  corre- 
spondingly. 

1 6.   The  Mathematical  Name 
of  the  figure  thus  produced  is 

Fig.  2.    Oblate  Spheroid.     ^^  ^^      The  apparatus 

shown  in  Fig.  3  strikingly  shows  the  effect  of  rotation 
upon  a  spherical  body.  Two  flexible  hoops  cross 

*  A  sphere  is  defined  as  a  figure  all  points  of  whose  surface  are 
equally  distant  from  a  point  within  called  the  centre. 


DEPARTURES  FROM  THE  SPHERICAL  FORM.    7 


each  other  at  right  angles,  and  through  their  points 
of  intersection  is  passed  a  vertical  rod.  When  the 
hoops  are  at  rest  they  occupy  the  positions  shown  by 
the  dotted  lines  ;  but  upon  being  rapidly  rotated,  they 
slide  down  upon  the  rod  and  assume  the  spheroidal 
form. 

1 7.  The  Amount  of  the  Flattening  at  the  Poles.  — 
The  difference  between  the  polar  and  equatorial  diam- 
eters of  the  earth  is  about  26  miles.     Each  pole,  then, 
is  depressed  only  about  13  miles,  a  distance  equal  to 
only  a  little  more  than  twice  the  height  of  a  very  high 
mountain. 

HOW   WE    KNOW    THAT    THE     EARTH     IS     FLATTENED    AT 
THE     POLES. 

1 8.  First  Proof.  —  Analogy.     We  have,  as  among 
the   proofs  of  its   spherical  form,  what  is  called  the 
argument   of    anal- 
ogy;  viz.,   all  rota- 
ting bodies  are  sub- 
ject to  the  law  that 

flattens  the  flexible 
hoops  (§  1 6).  We 
know  from  obser- 
vations of  the  disks 
of  other  heavenly 
bodies,  that  they  are 
obedient  to  the  law 
must  be  so  likewise. 

19.  Second     Proof.  —  Actual    Measurement.      A 
method  of  measuring  the  curvature  of  the  earth  was 


Fig.  3.     Effect  of  Rotation. 

hence  we  reason  that  the  earth 


8    DEPARTURES  FROM  THE  SPHERICAL  FORM. 

given  in  §  5  (Fig.  i).  Another  method  is  given  in 
§  44.  It  is  found  that  this  curvature  is  greatest  at  the 
equator,  and  that  it  grows  less  and  less  towards  the 
poles. 

20.  Third  Proof. —  Weight.  The  nearer  a  body 
above  the  surface  of  the  earth  is  to  the  centre,  the 
more  it  weighs.  It  is  found  that  a  body  weighs  a  little 
more  near  the  poles  than  at  the  equator ;  hence  we 
reason  that  the  poles  must  be  nearer  the  centre.* 

EXERCISES. 

I..  Estimating  the  earth's  diameter  at  8000  miles,  what  should 
be  the  thickness  of  a  grain  of  sand  to  represent  a  mountain  5 
miles  in  height,  upon  a  globe  6  inches  in  diameter?  Ans.  The 
height  of  the  mountain  is  5^7  of  the  earth's  diameter.  The 
thickness  of  the  grain  of  sand  must,  therefore,  be  -5-3-3-5  (j^ou) 
of  the  diameter  of  the  globe,  or  g-f  7  of  an  inch. 

2.  What  thickness  should  be  scraped  from  the  poles  of  the 
globe  to  represent  the  proper  amount  of  depression?     (§  17.) 

3.  What  should  be  the  width  and  depth  of  a  scratch  upon 
the  globe  to  represent  a  river  ^  of  a  mile  wide  and  T^  of  a  mile 
deep? 

4.  What  would  finally  result  if  the  rapidity  of  the  earth's 
rotation  should  be  indefinitely  increased?    Ans.   The  earth  would 
be  shattered,  and  its  fragments  would  be  hurled  into  space. 

5.  Of  what  material  is  the  earth's  axis  composed? 

6.  Would  the  earth  be  a  more  comfortable  or  beautiful  hab- 
itation for  us  if  its  form  were  changed  to  that  of  a  perfect 
sphere?     If  the  irregularities  were  made  very  much  greater  than 
they  are? 

*  Centrifugal  force  would,  of  course,  diminish  the  weight  some- 
what at  the  equator ;  but  nice  calculations  show  that  this  does  not 
account  for  all  the  difference  of  weight  in  the  two  positions. 


LATITUDE  AND  LONGITUDE.  9 

7.  Suppose  a  cloud  of  dust  were  thrown  from  the  earth  into 
space  with  sufficient  force  to  prevent  its  returning;  what  change 
would  take  place  in  the  size  of  the  mass?     In  its  form?     (§  4.) 

8.  Suppose   the   horizon  appeared  to  navigators  sometimes 
circular   and   sometimes   oval;    what  would   such   appearances 
imply  in  regard  to  the  form  of  the  earth?     (§  6.) 


III.   LATITUDE   AND   LONGITUDE. 

21.  Division  of  a  Spherical  Surface.  —  The  earth's 
surface  contains  about  200,000,000  square  miles.    The 
surface  of  a  sphere  cannot  be  laid  out  in  squares  like 
a  well-planned  city.     How  then  shall  we  lay  it  out? 
The  rotation  of  the  earth  furnishes  us  with  certain 
fixed  lines  and   points,  by  means  of  which  we  are 
enabled  to  lay  out  its  surface  even  more  easily  than  if 
it  were  a  vast  plane. 

22.  Poles,  Axis,  Equator,  etc.,  fixed  by  the  Earth's 
Rotation.  —  In  a  motionless  sphere  no  point  is  dis- 
tinguished from  the  rest  except  the  point  in  the  centre. 
When  rotation  begins,  however,  new  relations  are  im- 
mediately established.     Two  opposite  points  upon  its 
surface  remain  stationary,  which  are  called  the  poles. 
The  line  connecting  these  points,  also  stationary,  passes 
through  the  centre,  and  is  called  the  axis.     Points 
upon  the  surface  move  in  circles   around   the  axis, 
which  are  called  parallels  of  latitude.     These  increase 
according  to  their  distance  from  the  poles,  the  middle 
and  greatest  parallel  being  called  the  equator.    Circles 
drawn  upon  the  earth's  surface  through  the  poles  and 
cutting  the  parallels  and  equator  at  right  angles,  are 


10  LATITUDE  AND  LONGITUDE. 

called  meridian  circles.     Half  of  each  meridian  circle, 
extending  from  pole  to  pole,  is  called  a  meridian. 

23.  Planes  of  the  Equator,  Parallels,  etc. — We  may 
form  a  good  idea  of  a  plane  by  imagining  a  perfectly 
smooth  and  straight  sheet  of  glass  with  indefinite 
length  and  breadth,  but  without  appreciable  thickness. 
Such  planes  we  will  conceive  to  divide  the  earth  in 
different  parts.  The  plane  C,  Fig.  4,  cutting  the  sur- 


Fig.  4.    Planes  of  the  Equator  and  of  a  Parallel. 

face  through  the  equator,  is  called  the  plane  of  the 
equator ;  through  a  parallel,  D,  the  plane  of  a  par- 
allel, etc. 

The  figure  shows  the  planes  extending  to  but  a  short 
distance  beyond  the  earth's  surface.  There  is,  how- 
ever, no  limit  to  their  extent ;  the  plane  of  the  equator, 
for  example,  not  only  divides  the  earth,  but  it  may  be 
conceived  as  dividing  all  space  into  two  equal  parts. 
The  circle  in  which  this  plane  cuts  the  sky  is  called 
the  equinoctial  (§  69). 


LATITUDE  AND  LONGITUDE.  11 

24.  Latitude  is  distance  from  the  equator,  meas- 
ured in  degrees  on  a  meridian,  either  north  or  south. 
Thus,  the  north  pole  is  in  latitude  90°  north;    the 
tropic  of  Capricorn  is  in  latitude  23^°  south. 

25.  Longitude   is   distance   from   a  certain  fixed 
meridian,   measured  in  degrees  on  a  parallel,  either 
east  or  west. 

The  Prime,  or  First,  Meridian  is  the  fixed  meridian 
from  which  longitude  is  measured,  as  latitude  is  meas- 
ured from  the  equator.  If  there  were  a  certain  merid- 
ian naturally  distinguished  from  all  the  rest,  as  the 
equator  is  distinguished  from  all  the  other  parallels,  of 
course  it  would  be  selected  as  the  prime  meridian. 
But  there  is  no  such  meridian ;  all  are  of  the  same 
length,  and  we  can  distinguish  them  only  by  important 
places  through  which  they  pass.  Thus,  the  meridian 
which  passes  through  Washington  is  called  the  merid- 
ian of  Washington,  and  Americans  sometimes  measure 
from  this  as  the  prime  meridian.  More  commonly, 
however,  Americans  use  the  English  prime  meridian, 
which  passes  through  Greenwich.  Other  important 
nations  measure  from  their  own  capitals. 

26.  Having   the  Latitude  and  Longitude  of  a 
Place  given,  we  know  its  exact  position  upon  the 
earth's  surface,  and  can  find  it  upon  a  map  or  a  globe 
as  readily  as  we  can  find  a  house  by  its  street  and 
number,  or  a  soldier  by  his  regiment  and  company. 

27.  Significance  of  the  Names.  —  We  can  measure 
but  90°  from  the  equator,  while  we  may  measure  180° 
from  the  first  meridian.     Hence  the  former  distance 


12  LATITUDE  AND  LONGITUDE. 

is  called  latitude  (breadth),  and  the  latter,  longitude 
(length). 

28.  The  Length  of  Corresponding  Degrees  of  Lati- 
tude is  the  same,  on  whichever  meridian  they  may  be 
measured.     Near  the  poles  they  are  longer  than  near 
the  equator ;   but  the  difference  is  so  slight  as  to  be 
unimportant,  excepting  as  a  proof  of  the  spheroidal 
form  of  the  earth  (§  19). 

29.  The  Length  of  Degrees  of  Longitude.  —  Meas- 
ured on  the  equator  they  are  the  same  as  degrees 
of  latitude,  viz.,  -g^  the  circumference  of  the  earth. 
Measured  on  any  other  parallel  they  are  less,  since  the 
parallel  circle  itself  is  smaller  than  the  equator  or  a 
meridian  circle.     Hence  there  is  no  fixed  standard  of 
length  for  degrees  of  longitude,  which  vary  all  the  way 
from  69^  miles  at  the  equator  to  o  at  the  poles. 

30.  Maps  and  Mapped  Globes.  —  With  the  aid  of 
this  admirable  system  of  parallels  and  meridians,  it 
requires   only   accuracy   and   unwearied    industry   to 
enable  geographers  to  represent  on  maps  and  globes 
the  comparative  position,  extent,  and  outline,  or  form, 
of  the  continents,  islands,  countries,  seas,  etc.,  which 
variegate  the  immense  surface.     Should  they  attempt 
the  task  without  the  aid  of  these  guiding  lines,  they 
would  soon  find  themselves  lost  in  the  most  hopeless 
confusion. 

EXERCISES. 

1.  Can  a  place  be  farther  north  than  the  north  pole?     How 
many  degrees  of  north  latitude  are  there? 

2.  When  a  ship  is  sailing  directly  away  from  the  equator  — 
in  other  words,  when  it  is  "  making  latitude "  —  is  it  sailing 


ZONES.  13 

along  a  parallel,  or  a  meridian?     Then  is  latitude  measured  on 
a  parallel,  or  a  meridian? 

3.  Is  longitude  measured  on  a  parallel,  or  a  meridian? 

4.  A  certain  vessel  was  wrecked  in  latitude  10°  south,  longi- 
tude 10°  west  from  Greenwich.     Near  what  land  was  it? 

5.  In  what  longitude  is   New  York  City,   measuring   from 
Greenwich?     From  Washington?     From  Paris? 

6.  Is  the  iSoth  degree  of  longitude  east,  or  west,  longitude? 

7.  In  what  longitude  are  the  poles? 

8.  If  a  vessel  should  sail  directly  north  from  the  equator, 
steering  in  the  same  direction  until  it  has  passed  over  a  space 
equal  to  100°,  in  what  latitude  would  it  be? 

9.  A  vessel  sails  due  west  from  the  meridian  of  Greenwich, 
over  200°  of  the  parallel;    in  what  longitude  is  it  from  Green- 
wich? 

10.  How  far  apart  may  two  points  be,  and  yet  be  in  the  same 
latitude? 

1 1 .  How  far  apart  may  two  points  be,  and  yet  be  in  the  same 
longitude? 

12.  How  many  meridians  may  be  drawn  through  a  parallel? 

13.  How  many  parallels  may  be  drawn  through  a  meridian? 

14.  How  many  miles  in  a  degree  of  latitude? 

15.  What  is  the  length,  in  miles,  of  a  degree  of  longitude 
measured  on  the  equator? 

1 6.  About  what  part  of  a  mile  does  a  degree  of  longitude 
measure  on  the  parallel  seven  miles  distant  from  the  pole  ?    (  Con- 
sider the  space  within  the  circle  flat,  and  multiply  the  diameter 
of  the  circle  by  34,  to  obtain  its  approximate  circumference?) 


IV     ZONES. 

31.  Meaning  of  "Zone."  —  If  the  space  between 
two  parallel  circles  upon  the  surface  of  a  sphere  be 
distinguished  from  the  rest  of  the  surface,  it  will  pre- 


14  ZONES. 

sent  the  appearance  of  a  belt  encircling  the  sphere ; 
hence  the  name  zone  (belt) . 

32.  Number  and  Names  of  the  Zones.  —  The  sur- 
face of  the  earth  is  divided,  by  four  parallel  circles, 
into  five  zones,  viz.,  North  Frigid,  North  Temperate, 
Torrid,  South  Temperate,  and  South  Frigid.    The  four 
dividing  circles  are  the  Tropics  and  the  Polar  Circles. 

THE  ZONES  ARE  NATURAL  DIVISIONS  OF  THE  EARTH'S 
SURFACE. 

33.  The   Torrid   Zone. — The   sun's  vertical   rays 
do   not   always   fall   upon   the   equator.      Sometimes 
they  fall  upon  the  parallel  23^°  north  of  the  equator 
—  the  Tropic  of  Cancer;   at  other  times,  upon  the 
parallel   23^-°  south  of  the   equator  —  the  Tropic  of 
Capricorn ;  and,  in  the  meantime,  upon  every  circle 
between  these  two.     But  they  never  fall  farther  north 
or   south   than  the  tropics.       (These  northward  and 
southward  movements  of  the  sun  will  be  described 
more  fully,  and  their  causes   explained,  in   a  future 
section.)     Now,  the  solar  light  and  heat  are  the  most 
intense  where  the  vertical  rays  fall ;  hence  these  rays 
mark  off  a  zone  of  the  earth's  surface  47°  in  breadth, 
divided  from  the  rest  of  the  surface  by  the  tropics. 
This  is  called  the  Torrid  (or  hot]  Zone. 

34.  The  Frigid  Zones.  —  For  the  same  reason  that 
the  vertical,  or  hottest,  rays  of  the  sun  do  not  always 
fall  upon  the  equator,  the  most  Dblique,  or  coldest,  rays 
do  not  always  fall  at  the  poles.     And  as  the  vertical 
rays  range  23^°  from  the  equator,  so  the  most  oblique 


ZONES.  15 

rays  range  23^°  from  the  poles.  Hence  these  rays 
mark  off  two  sections  of  the  earth's  surface,  each  47° 
in  diameter,  and  divided  from  the  rest  by  the  Arctic 
and  Antarctic  circles.  These  are  called  the  Frigid 
(or  cold)  Zones. 

35.  The  Temperate  Zones. — Between  the  Torrid 
and  the  Frigid  lie  the  Temperate  Zones,  upon  which 
neither  the  vertical  nor  the  most  oblique  rays  of  the 
sun  fall,  that  is,  neither  the  hottest  nor  the  coldest 
rays,  hence  their  name. 

Exercise.  — What  is  the  breadth  of  the  Temperate  Zones? 

36.  The  Difference  between  the  Climate  of  the 
Torrid  and  that  of  the  Frigid  Zones  is  so  great  that, 
if  animals  belonging  to  one  should  be  carried  to  the 
other,  they  would  soon  perish  ;  and,  while  the  rankest 
luxuriance  of  vegetation  grows  in  one,  there  are  but  a 
few  hardy  shrubs  and  mosses  to  vary  the  eternal  snows 
of  the  other. 

37.  The  Reasons  for  this  Great  Difference  may  be 
easily  understood  from  Figs.  10  and  n,  and  the  para- 
graphs relating  to  them. 

38.  Gradual  Decrease  in    Temperature  from   the 
Equator  to  the  Poles.  —  Representations  of  the  earth, 
with  the  zones  painted  upon  its  surface,  imply  very 
abrupt  changes  at  the  dividing  circles ;  but,  of  course, 
no  more  sudden    change  would   actually  be  experi- 
enced in  crossing  these  dividing  circles  than  in  cross- 
ing any  other  parallels. 


16  DIMENSIONS  AND  DISTANCES. 


V.    DIMENSIONS  AND   DISTANCES. 

39.  The  Circumference  of  the  Earth  is,  in  round 
numbers,  25,000  miles. 

40.  The  Diameter  is  a  little  less  than  one-third  of 
the  circumference,  or  about  8,000  miles.    (See  Appen- 
dix, I.) 

41.  The  Earth's  Distance  from  the   Sun  varies 
slightly  during  the  year,  the  greatest  distance  {Aphe- 
lion, §  75)  being  estimated  at  94,500,000  miles;  and 
the   least    {Perihelion) ,  at   91,500,000    miles.      The 
average   or   mean   distance  is,  therefore,  93,000,000 
miles.     (See  Appendix,  II.) 

42.  The  Earth  in  Space.  —  The  earth  seems  to  us 
an  immense  body,  yet  it  is  one  of  the  smallest  of  the 
bodies  that  roll  in  space.     In  fact,  the  whole   solar 
system  taken  together  is  but  a  mere  point  when  com- 
pared with  the  universe. 

As  the  student  of  botany  regards  some  insignificant 
plant  as  only  an  individual  of  an  innumerable  species, 
so  let  us  regard  the  earth  as  only  a  small  specimen  of 
countless  myriads  formed  on  the  same  general  plan. 

HOW  WE  KNOW  THE   MAGNITUDES  AND  DISTANCES  OF 
THE  HEAVENLY  BODIES. 

43.  Measurement  of  the  Earth.  —  First  Method. 
The  amount  of  curvature  of  a  small  portion  of  the  sur- 
face may  be  measured  as  shown  in  §  5,  Fig.  i,  and 
from  this  arc  the  whole  circumference  may  be  found. 


DIMENSIONS  AND  DISTANCES.  17 

Exercise.  — A  peak  of  the  Andes  4  miles  high  is  just  visible 
on  the  Pacific  Ocean  at  the  distance  of  178^  miles.  This  gives 
an  arc  of  a  circle  equal  to  2.58  degrees.  How  many  miles  in 
360  degrees?  Arts.  24,872+  miles. 

44.  Second  Method.  —  The  north  star  remains  ap- 
parently motionless  in    the    sky,  excepting  when  we 
move  towards  or  from  it.     If  we  sail  towards  it  over 
one  degree  of  latitude,  it  seems  to  ascend  one  degree 
towards  the  zenith.     To  cause  this  appearance,  it  is 
found  that  a  ship  must  sail  about  69^  miles  directly 
north  —  one  degree  of  latitude.     Multiplying  this  by 
360,  we  have  the  circumference,  24,900  miles. 

45.  f1  Estimation  of  Distances.  —  In  giving  us  two 
eyes,  nature    has  enabled   us    to    measure  very  accu- 
rately the  distances  of  objects  immediately  around  us. 

Hold  your  finger  very  near  your  eyes  (Fig.  5).  To 
look  directly  at  it,  you  must  turn  your  eyes  inward, 
in  other  words,  look  "  cross-eyed."  Now  look  beyond 
your  finger  at  a  wall  or  a  window.  The  finger  will  ap- 
pear in  two  different  positions  against  the  wall  or  win- 
dow. Close  the  right  eye,  and  it  will  appear  against 
A.  Close  the  left  eye,  it  will  appear  against  B.  The 
farther  you  remove  your  finger  from  your  eyes,  the  less 
you  have  to  turn  your  eyes  inward  to  look  at  it,  and 
the  shorter  grows  the  line  AB  on  the  window  (called 
the  parallax] .  In  general,  the  less  we  have  to  turn 
our  eyes  inward,  or  towards  each  other,  to  look  at  an 
object,  the  farther  off  we  judge  it  to  be ;  in  other 
words,  the  less  its  parallax  becomes. 

Exercise.  —  How  far  off  must  a  point  be  in  order  that  the 
eyes  must  look  in  exactly  parallel  lines  to  look  directly  at  it? 

1  See  Preface. 


18  DIMENSIONS  AND  DISTANCES. 

The  farther  apart  our  eyes  are,  the  more,  of  course, 
we  have  to  turn  them  inward  to  look  at  an  object,  and 
the  better  judges  of  distance  we  are.  Our  eyes  are 
too  near  together  to  serve  in  this  way  for  great  dis- 
tances. Thus,  the  heavenly  bodies  all  appear  at  the 
same  distance  from  us,  although  their  real  distances 
are  immensely  different.  Still,  we  can  apply  the  prin- 
ciple in  a  different  way.  Fig.  6  represents  two  men 


Fig.  5.     Estimating  Distances. 

measuring  the  distance  of  a  balloon.  Knowing  their 
own  distance  apart  (AB,  the  "base  line"),  and  find- 
ing how  much  they  have  to  turn  towards  each  other  to 
look  directly  at  the  balloon,  they  can,  by  a  mathemati- 
cal process  too  difficult  to  explain  here,  calculate  its 
distance  precisely  as  you  judge  of  the  distance  of  your 
finger  by  the  angle  at  which  you  have  to  incline  your 
eyes  inward  to  see  it.  Observe  that  the  arc  CD 
(Fig.  6)  in  the  sky  is  the  parallax  of  the  balloon,  just 
as  AB  (Fig.  5)  is  that  of  the  finger  on  the  window. 


DIMENSIONS  AND  DISTANCES. 


19 


20  DIMENSIONS  AND  DISTANCES. 

The  farther  away  an  object  is,  the  greater  must  be 
the  base  line  (AB,  Fig.  6)  to  measure  its  distance. 
In  the  cases  of  the  sun  and  the  nearer  planets  the 
base  line  used  is  half  the  diameter  (radius)  of  the 
earth  —  4,000  miles. 

Exercises. —  I.  If  ABC  (Fig.  7)  represents  the  earth,  and 
S  the  sun,  what  line  represents  the  sun's  parallax  in  the  sky? 

2.  If  the  sun  were  removed  farther  from  the  earth,  would 
this  line  increase  or  diminish? 


Fig.  7.     The  Parallax  of  the  Sun. 

46.   t1  Measuring  the  Size  of  the  Sun  and  Moon.  — 

Having  thus  found  the  distances  of  these  bodies,  we 
can  measure  their  diameter  as  follows :  Place  a  cir- 
cular piece  of  paper  before  one  eye  at  such  a  distance 
that  it  will  exactly  conceal  the  moon,  for  example, 
from  view.  Now  a  circle  twice  as  far  away  would  have 
to  be  of  just  twice  the  diameter  to  fill  the  same  space 
in  the  eye ;  one  as  far  away  as  the  moon  would  have 
to  be  as  many  times  as  great  in  diameter  as  the  moon's 
distance  is  greater  than  that  of  the  paper  circle. 

Exercise.  —  If  a  paper  disk  I  inch  in  diameter  be  pasted  on 
a  window-pane  in  view  of  the  full  moon,  a  spectator  will  have  to 
withdraw  9^7  feet  from  the  paper  disk  in  order  that  it  may  just 
conceal  the  moon  from  his  sight.  Required,  the  moon's  diameter. 

1  See  Preface. 


THE   SUN  AND    THE  ATMOSPHERE.          21 

Ans.  The  moon's  distance  being  240,000  miles,  or  136,857,- 
600  times  greater  than  that  of  the  paper  disk,  its  diameter  must 
also  be  the  same  number  of  times  greater  than  that  of  the  paper 
disk, —  136,857,600  X  i  inch  =2,160  miles. 


VI.  THE  SUN'S  RAYS  AND  THE  EARTH'S 
ATMOSPHERE. 

47.  Light  is  the  Means  of  Sight,  although  itself 
Invisible. — We  often  speak  of  "seeing  light";  but 
it  is  not  light  that  we  see,  but  the  various  objects  which 
send  light  to  our  eyes.     Light  is  not  a  substance ;  it 
is  only  a  means  which,  by  affecting  our  eyes,  enables 
us  to  see  substances.     If  there  were  no  substance  in 
view,  we   should   be   surrounded    by   darkness,   even 
though  the  space  around  us  were  filled  with  rays  of 
light. 

48.  Examples  showing  that  we  do  not  see  Light. — 
i .  If  we  stand  before  a  brilliantly  lighted  window  upon 
a  dark  evening,  the  rays  from  within  will  pour  upon  us 
in  a  flood,  and  the  space  between  us  and  the  window 
will  seem  bright  with  the  light.     But  if  we  move  to  a 
corner  of  the  building  so  that  the  window  itself  shall 
not  be  within  the  range  of  vision,  the  space  in  front  of 
it,  if  the  air  is  perfectly  clear,  will  seem  as  dark  as  if 
the  window  were  unlighted ;   we  cannot  see  the   rays 
pouring  out  into  that  space.     If,  however,  some  sub- 
stance move  into  the  space,  as  a  passing  carriage  or 
even  a  cloud  of  mist,  it  will  be  suddenly  lighted  up. 
The  rays  will  enable  us  to  see  the  substance. 


22 


THE  SUN  AND    THE  ATMOSPHERE. 


2.  At  midnight,  when  the  sun  is  far  below  the  hori- 
zon, his  rays  must,  of  course,  shoot  up  on  all  sides  of 
the  earth,  as  shown  in  Fig.  8 ;  and  if  these  rays  could 
be  seen,  they  would  present  the  appearance  of  a  daz- 
zling shower  pouring  up  from  the  horizon  on  all  sides, 
causing  the  night  to  be  nearly 
as  bright  as  the  day.  At  mid- 
night, however,  we  see  no  evi- 
dence of  the  sun's  rays,  unless 
there  be  some  siibstance  above 
us,  like  the  moon  or  the  plan- 
ets, to  receive  the  rays  and 
throw  them  back  to  us. 

49.  Air*  in  Large  Quanti- 
ties is  Visible,  and  is  of  a  pale 
blue  color.  We  look  upward 
in  the  daytime,  and  see  what 
seems  to  us  an  immense  flood 
of  pure  light.  Of  what  is  this 
vast  illuminated  ocean  com- 
posed, whose  upper  surface 
seems  a  shell  of  pale  blue? 
It  cannot  be  light  that  we  see,  for  we  have  shown 
light  to  be  invisible.  Plainly  then  it  must  be  some 
substance  lighted  by  the  sun's  rays,  just  as  a  cloud 
of  mist  would  be  lighted  by  a  candle. 

That  substance  is  the  air.  If  it  were  removed,  the 
flood  of  light  would  disappear,  and  we  should  see 
nothing  above  us,  even  at  noon,  but  a  black,  measure- 


Fig.  8. 


*  Including  all  the  various  solid  and  liquid  particles  which  the 
atmosphere  contains. 


THE  SUN  AND    THE  ATMOSPHERE.          23 

less  abyss,  with  the  sun  glaring  in  the  midst,  and  the 
stars  and  the  moon  as  plainly  visible  as  they  are  now 
at  night. 


9.    The  Earth's  Atmosphere  illuminated  by  the  Sun's  Rays. 


50.  Why  we  do  not  realize  that  the  Air  is  Visible.  — 
This  is  because  we  have  nothing  more  transparent  than 
itself  with  which  to  contrast  it.  If  a  great  ball  of  air 


24  THE   SUN  AND    THE  ATMOSPHERE. 

could  be  suspended  in  empty  space  beyond  our  at- 
mosphere, we  should  see  it  shining  at  night  like  a 
planet. 

Fig.  9  shows  the  air  thus  lighted  by  the  sun's  rays. 
The  halo,  represented  as  half  surrounding  the  earth, 
may  be  regarded  as  a  picture  of  the  flood  of  light 
which  we  see  above  us  in  the  daytime,  and  which 
would  disappear  if  the  air  were  removed.  If  we  could 
ascend  above  this,  we  should  see  the  black,  starry 
space  beyond,  as  is  proved  by  those  who  make  balloon 
ascensions  or  climb  lofty  mountains.  These  men 
describe  the  sky  growing  darker  and  darker,  as  they 
leave  more  and  more  of  the  atmosphere  below  them, 
until  the  stars  become  visible  even  at  noonday. 

Fig.  8  is  an  example  of  the  manner  in  which  light  is 
usually  represented.  It  will  be  understood,  however, 
that  only  the  directions  of  the  rays  are  shown  by  the 
straight  lines,  as  the  directions  of  the  equator,  ecliptic, 
etc.,  are  shown  by  curved  lines. 

51.  The  Speed  of  Light  is  about  186,000  miles 
a  second.     It  requires,  therefore,  a  little  more  than 
eight  minutes  for  a  ray  of  light  to  reach  us  from  the 
sun. 

GRADUAL  CHANGES  IN  LIGHT  AND  HEAT  DURING  THE 
DAY  AND  THE  YEAR. 

52.  Twilight  is  the  gentle  sunlight  that  plays  around 
us  before  sunrise  and  after  sunset.     It  is  nothing  more 
than  the  gray  border  of  the  "  flood  of  light,"  described 
in  §  49  and  represented  in  Fig.  9. 


THE  SUN  AND    THE  ATMOSPHERE.         25 

How  Twilight  is  produced.  —  Long  before  the  sun's 
direct  rays  reach  us  they  shine  upon  the  upper  regions 
of  the  air  in  the  east,  and  produce  the  first  gray  streaks 
of  dawn.*  We  see  this  brightened  air  in  the  distance 
just  as  we  see  the  tops  of  distant  mountains  lighted 
up  before  sunrise  and  after  sunset.  As  the  sun  rises 
higher  and  higher  towards  the  horizon,  more  and  more 
of  the  air  above  our  heads  becomes  lighted  up,  until 
at  the  appointed  instant  his  broad  disk  bursts  into  view. 

53.  The  Day.  —  Even  then  we  have  not  the  full 
light  of  day.     We  may  gaze  upon  the  very  face  of  the 
sun,  and  scarcely  feel  his  warmth.     As  he  makes  his 
sublime  ascent  he  becomes  more  and  more  powerful 
until  he  reaches  his  culmination,  after  which  his  power 
as  gradually  diminishes,  till  the   second  twilight  has 
faded  away  into  the  darkness  of  night. 

54.  The  Year  presents  similar  gradual  changes  in 
light  and  heat,  and  the  changes  of  both  the  day  and 
the  year  are  due  to  the  same  cause,  viz.,  differences 
in  the  direction  of  the  sun's  rays. 

Two  REASONS  WHY  DIFFERENCES  IN  THE  DIRECTION 
OF  THE  SUN'S  RAYS  MAKE  DIFFERENCES  IN  THEIR 
POWER. 

55.  First:   The  more  slanting  the  rays,  the  greater 
the  surface  over  which  they  are  scattered,  and  hence 
the  less  intense  their  power. 

Fig.  10  represents  three  sheaves,  or  bundles,  of  the 
sun's  rays,  striking  the  earth  at  three  different  periods 

*  Twilight  begins  when  the  sun  is  about  18°  below  the  horizon. 


26  THE  SUN  AND    THE  ATMOSPHERE. 

of  the  day.  At  noon  the  rays  are  nearly  vertical,  and  fall 
upon  the  surface  between  C  and  D.  In  the  middle  of 
the  afternoon  they  are  inclined,  and  are  spread  over  a 
greater  surface,  DE.  At  sunset  the  lower  side  of  the 


Fig.  10.    Dispersion  of  Rays  over  Surface. 

sheaf  just  touches  the  surface,  while  most  of  the  rays 
themselves  are  lost  in  the  space  beyond. 

56.  Second:  The  more  slanting  the  rays,  the  more 
air  they  must  pass  through,  and  therefore  the  more 
they  are  interrupted  and  absorbed. 

We  have  already  learned  that  the  air  is  not  perfectly 
transparent ;  it  interrupts  the  light  as  glass  interrupts 
it,  though  not  in  so  great  a  degree.  A  clear  pane  of 
glass  seems  to  admit  as  much  light  as  an  open  space 
of  equal  extent ;  but  if  it  were  a  hundred  times  as 
thick  it  would  admit  scarcely  any  light.  So  if  the  air 
were  sufficiently  increased  in  quantity  we  should  be 
left  in  utter  darkness,  as  if  we  were  at  the  bottom  of 


THE  SUN  AND    THE  ATMOSPHERE.         27 

the  ocean.  When  we  look  at  the  sun  in  the  horizon, 
we  see  him  through  an  immense  mass  of  air ;  hence 
he  sometimes  appears  of  a  dull  red  color,  as  if  seen 
through  smoked  glass. 


Fig.  ii.    Interruption  of  Rays  by  the  Atmosphere. 

57.  In  Fig.  ii,  SBA  represents  a  noon  ray  of  sun- 
light, and  S'  DA  one  at  sunrise  or  sunset.  If  the 
curved  line  BD  represent  the  outside  of  the  atmos- 
phere, fifty*  miles  above  the  surface  of  the  earth,  it  is 

*  Fifty  miles  is  the  height  formerly  assigned  to  the  atmosphere, 
although  it  probably  stretches  off,  in  a  state  of  extreme  rarity,  many 
hundred  miles  beyond  this  limit,  gradually  shading  off  into  nothing- 
ness. Its  great  mass,  however,  is  within  eight  or  ten  miles  of  the 
earth's  surface,  the  more  elevated  portions  comparing  with  the 
lower  very  much  as  the  vapor  of  the  ocean  compares  with  the  ocean 
itself. 


28  THE  EARTH'S  DAILY  MOTION. 

evident  that  the  rays  must  penetrate  through  very 
much  more  air  when  the  sun  is  in  the  horizon  than 
when  he  is  overhead. 


VII.    THE   EARTH'S   DAILY   MOTION. 

58.  The  Earth  performs  Two  Motions.  —  It  rotates 
upon  its  axis  once  in  twenty-four  hours,  and  it  revolves 
around  the  sun  once  a  year. 

59.  The  Motions  are  Permanent.  —  Nothing  made 
by  man  will  continue  in  motion  indefinitely,  unless 
new  force  is  repeatedly  applied  to  it.     A  watch  will 
stop  unless  it  is  wound  at  regular  intervals,  and  even 
then  it  will  finally  wear  out.     But   the  earth  never 
wears,  and  will  never  stop  unless  some  great  change 
takes  place  in  nature  to  produce  such  a  result. 

60.  What  keeps  the  Earth  moving?  —  A  top  will 
spin  much  longer  on  a  smooth  surface  than  on  a  rough 
one;    it  will  spin   scarcely  a  second  of  time  under 
water.     Having  been  set  in  motion,  the  length  of  time 
during  which  it  will  continue  moving  depends,  first, 
on  the  amount  of  friction  between  the  peg  of  the  top 
and  the  surface  on  which  it  spins ;   secondly,  on  the 
density  of  the  medium  in  which  it  spins.     Suppose 
the  top  to  be  spinning  in  a  perfectly  empty  space  with- 
out friction  or  any  other  resistance  to  overcome,  how 
long  will  it  continue  in   motion?  —  a  day?    a  year? 
What  will  then  cause  it  to  stop  ?     It  will  require  as 
much  force  to  destroy  its  motion  as  was  required  in 


THE  EARTH'S  DAILY  MOTION.  29 

the  first  place  to  produce  it,  and  unless  that  force  is 
applied,  it  will  continue  spinning  forever. 

The  earth  is  like  a  huge  top  in  precisely  similar  cir- 
cumstances. It  rotates  in  empty  space,  and  there  is 
no  friction  between  its  surface  and  any  external  sur- 
face, as  there  is  between  the  peg  of  the  top  and  the 
floor.  But  does  not  the  air  resist  the  motion  of  the 
earth  as  it  resists  that  of  the  top  ?  By  no  means ; 
the  air  is  a  part  of  the  earth  —  a  thin  covering  — 
and,  like  the  ocean,  is  carried  around  with  it. 

The  same  principle  applies  to  the  earth's  motion 
around  the  sun  as  to  its  rotation.  It  continues  undi- 
minished  simply  because  there  is  nothing  to  resist  it. 

61.  The  Effects  of  the  Earth's  Rotation :  — 

(1)  Alternation  of  day  and  night  (§  62). 

(2)  Determination  of  an  axis,  equator,  etc.  (§  22). 

(3)  Flattening  at  the  poles  (§  16). 

(4)  Apparent  rotation  of  the  heavens  in  the  oppo- 
site direction  (§66). 

62.  The  Alternation  of  Day  and  Night.  —  As  the 
sun  shines  on  only  one-half  the  earth's  surface  at  a 
time,  the  other  half  must  be  in  darkness.     If  there 
were  no  motion  one  half  would  be  in  constant  day  and 
the  other  half  in  constant  night ;   but  the  rotation  of 
the  earth  brings  each  half,  in  turn,  into  the  light  and 
shade. 

EXERCISES. 

1.  When  it  is  noon  at  Boston,  where  on  the  same  parallel  is  it 
sunrise?     Sunset?     Midnight?     [In  the  questions  I  and  2  the 
sun  is  supposed  to  be  over  the  equator.] 

2.  When  it  is  sunrise  at  London,  where  on  the  same  parallel 
is  it  noon?     Sunset?     Midnight? 


30  THE  EARTH'S  DAILY  MOTION. 

3.  Over  how  much  of  a  meridian  is  it  noon  at  the  same 
instant? 

4.  Over  how  much  of  a  parallel  is  it  noon  at  the  same  instant? 

5.  How  many  miles  an  hour  does  a  body  at  the  equator  move 
around  the  earth's  axis? 

6.  If  a  man  or  an  animal  should  perform  this  rapid  motion 
through  the  air  would  he  be  likely  to  feel  the  resistance?     Ans. 
The  effect  would  be  very  much  greater  than  that  of  the  most 
violent  hurricane. 

7.  Then  does  the  earth  move  through  the  air,  or  does  the  air 
move  with  the  earth  ? 

8.  What  is  the  rate  of  motion  at  the  poles? 

9.  Is  the  rate  of  motion  on  the  parallel  ten  miles  from  the 
poles  very  rapid,  or  slow? 

63.  Belief  of  the  Ancients. — The  ancients  gener- 
ally supposed  that  the  earth  is  perfectly  motionless, 
and  that  the  sun,  moon,  and  stars  perform  daily  revo- 
lutions around  it. 

Insensible  Motion  often  causes  a  Similar  Delusion. — 
The  motion  of  a  balloon  through  the  air  is  so  extremely 
gentle,  however  rapid  it  may  be,  that  if  one  closes  his 
eyes  or  looks  only  at  the  sky  it  seems  motionless ;  and 
upon  looking  downward  the  sensation  is  strong  that 
the  earth  is  falling  away  from  the  balloon,  rather  than 
that  the  balloon  is  rising  above  the  earth.  Although 
we  are  totally  insensible  of  the  earth's  motion,  yet  we 
feel  that  it  would  be  almost  as  absurd  for  us  to  regard 
the  earth  as  stationary  and  the  heavens  in  motion 
around  it,  as  for  the  aeronaut  to  regard  his  balloon  as 
fixed  and  the  earth  descending  below  it.  But  we  are 
not  obliged  to  content  ourselves  with  mere  proba- 
bilities ;  the  earth's  rotation  is  proved  to  a  positive 
certainty. 


THE  EARTH'S  DAILY  MOTION. 


31 


HOW   WE   KNOW   THAT   THE    EARTH   ROTATES. 

64.  First :  We  have  seen  on  what  principle  the  dis- 
tances of  the  heavenly  bodies  may  be  measured.     We 
know  that  the  stars  are  so  distant  that  their  light,  whose 
motion  is  inconceivably  swift,  requires  years  to  reach 
us ;  yet  they  seem  to  move  around  the  earth  once  in 
twenty-four  hours.     We  know  that  it  is  impossible  for 
them  actually  to  perform  such  motions.      The  only 
way,  therefore,  by  which  the  appearances  can  be  pro- 
duced is  by  the  earth  itself  turning  on  its  axis. 

65.  Secondly :  When  a  grindstone  is  rotating  rapidly, 
it  will  throw  drops  of  water  in  the  direction  in  which 
it    is    rotating ;     if, 

for  example,  its  up- 
per surface  is  mov- 
ing toward  the  east, 
it  will  throw  the 
drops  eastward.  The 
earth  does  precisely 
the  same  thing.  A 
stone  dropped  from 
the  top  of  a  high 
cliff  always  falls  a 
little  east  of  a  verti- 
cal line ;  that  is,  it  is  thrown  a  little  eastward  by  the 
earth's  rotation  (Fig.  12). 

If  the  earth's  rotation  were  as  rapid  in  proportion  as 
that  of  the  grindstone  which  throws  off  drops  of  water, 
objects  on  its  surface  would  be  thrown  off  in  the  same 


Fig.  12.     Proof  of  Earth's  Rotation. 


32  THE  EARTWS  DAILY  MOTION. 

way.  A  stone,  for  example,  would  fly  from  the  cliff 
(Fig.  12)  in  the  horizontal  line  AE,  towards  the  east. 
As  the  rotation  is  not  nearly  so  rapid,  however,  the 
stone's  departure  from  the  vertical  line  AC  in  fall- 
ing is  comparatively  slight.  Thus  the  distance  CD 
furnishes  mathematicians  with  an  independent  means 
of  determining  the  rate  of  the  earth's  rotation. 

(For  Foucault's  famous  experiment  proving  the 
earth's  rotation,  see  Appendix  III.) 

APPARENT  DAILY  MOTION  OF  THE  HEAVENS. 

66.  Different  Rates  of  Apparent  Motion  of  the 
Stars,  etc. — Among  the  effects  of  the  earth's  daily 
motion  is  the  apparent  daily  rotation  of  the  starry 
sphere  (with  the  sun,  moon,  etc.)  in  the  opposite 
direction,  from  east  to  west.  The  same  principles 
apply  to  this  apparent  motion  that  apply  to  the  rota- 
tion of  any  sphere,  viz.,  the  poles  (the  north  star* 
and  the  opposite  point  in  the  heavens)  remain  station- 
ary, merely  turning  upon  themselves  as  upon  pivots, 
while  the  rate  of  apparent  motion  increases  accord- 
ing to  the  distance  from  the  poles,  being  swiftest  at 
the  celestial  equator,  or  equinoctial,  which  lies  over  the 
earth's  equator  as  the  celestial  poles  stand  over  the 
earth's  poles.  Stars  near  the  pole  star  seem  to  move 
in  small  circles  around  it  every  twenty-four  hours,  pre- 
cisely as  icebergs  are  carried  by  the  earth's  rotation 

*  The  north  star  is  at  a  very  slight  distance  (15°)  from  the  true 
north  pole  of  the  heavens.  Consequently,  it  seems  to  describe  a 
minute  daily  circle  around  it. 


THE  EARTH'S  DAILY  MOTION.  33 

around  the  north  pole,  only  in  the  opposite  direction ; 
stars  farther  off  describe  larger  circles,  those  over  the 
equator  describing  the  largest  of  all. 

67.  How  to  observe  the  Apparent  Rotation  of  the 
Heavens.  —  Most  persons  know  where  to  look  among 


Fig.  13.     Apparent  Daily  Motion  of  the  Heavens. 

the  stars  for  the  "  Dipper."  It  is  represented  in  Fig. 
13,  ABD.  The  two  stars  A  and  B  are  called  "point- 
ers," because  they  seem  to  point  to  the  pole  star  P. 


34  THE  EARTH'S  DAILY  MOTION. 

The  circles  in  the  figure  show  the  apparent  revolution 
of  the  stars,  or  the  rotation  of  the  celestial  sphere  in 
the  direction  of  the  arrows,  from  east  to  west. 

Now,  on  some  clear  evening  carefully  observe  the 
relative  positions  of  the  Dipper  and  some  other  cluster, 
as  Cassiopeia,  M,  which  resembles  an  irregular  W  in 
form.  The  book  can  easily  be  held  so  that  the  stars 
in  the  figure  shall  correspond  in  position  with  those  in 
the  sky.  Observe  also  the  positions  of  certain  bright 
stars  overhead  and  near  the  eastern  and  western  hori- 
zon. Compare  their  positions  again  about  three  hours 
afterwards.  The  north  star  will  not  appear  to  have 
moved,  the  Dipper  will  have  moved  through  T\,  or  £, 
of  the  whole  circle,  and  the  pointers  will  be  at  E  and 
F.  All  the  other  stars  will  also  have  moved  through  \ 
of  their  circles,  those  that  were  in  the  eastern  hori- 
zon having  ascended,  those  that  were  overhead  having 
descended  toward  the  west,  and  those  that  were  in  the 
western  horizon  having  set. 

68.  Circles  of  Perpetual  Apparition  and  Occupa- 
tion. —  The  stars  within  the  heavily  marked  circle  G, 
Fig.  13,  never  pass  below  the  horizon  by  day  or  by 
night.  This  circle  is,  therefore,  called  the  circle  of 
Perpetual  Apparition  (appearance) .  What  represents 
the  circle  of  perpetual  apparition  in  Fig.  17?  The 
south  pole  of  the  heavens  is  as  far  below  the  horizon 
as  the  north  pole  is  above  it ;  there  must,  therefore, 
be  a  circle  around  the  south  pole  corresponding  to 
G  in  which  to  us  the  stars  never  rise.  This  is  called 
the  circle  of  Perpetual  Occupation  (concealment). 
Both  these  circles  increase  as  we  move  towards  the 
poles,  and  diminish  as  we  move  from  them. 


THE  EARTH'S  DAILY  MOTION.  35 

69.  Daily  Motion  of  the  Heavens  as  seen  from 
Different  Points  of  the  Earth's  Surface.  —  Fig.  14 
represents  the  earth  in  the  centre  of  the  hollow  sphere 
of  the  heavens;  PP'  are  the  poles  of  the  heavens 


Fig.  14.    Earth  in  Centre  of  Celestial  Sphere. 

directly  over  the  poles  of  the  earth,  and  EQ  is  the  celes- 
tial equator,  or  equinoctial,  over  the  earth's  equator. 

From  the  North  Pole.  —  If  we  should  stand  at  N, 
Fig.  14  or  Fig.  15,  our  horizon  would  coincide  with 
the  equinoctial ;  the  north  star,  P,  would  be  directly 
overhead  •  and  the  other  stars,  with  the  sun,  moon, 
and  planets,  would  seem  to  move  in  circles  around 
us  —  aa',  bb\  cc\  etc. 


36 


THE  EARTH'S  DAILY  MOTION. 


From  the  Equator.  —  If  we  should  stand  at  E,  Fig. 
14  (hold  the  page  so  that  Q  shall  be  uppermost),  or 
at  X,  Fig.  1 6,  the  north  star  would  be  exactly  in  the 
northern  horizon,  and  the  other  stars,  sun,  moon,  etc., 
would  seem  to  move  in  circles  perpendicular  to  the 
horizon. 


Fig.  15.    Daily  Motion  of  Heavens  as  seen  at  the  North  Pole. 

From  a  Point  between  the  Equator  and  a  Pole.  —  It 
we  should  stand  at  a  point  between  the  equator  and 
the  north  pole,  as  at  X,  Fig.  17,  the  north  star,  P, 
would  be  seen  at  a  distance  above  the  horizon  corre- 
sponding to  our  distance  from  the  equator  (§71,  see 
also  Fig.  13)  ;  and  the  other  stars,  sun,  moon,  etc., 
would  seem  to  move  in  circles  oblique  to  the  horizon. 

70.  How  Long  does  a  Heavenly  Body  remain 
above  the  Horizon  ?  —  Questions  : 

i.   During  what  portion  of  the  twenty-four  hours  of 


THE  EARTH'S  DAILY  MOTION. 


37 


the  day  does  the  sun,  moon,  or  a  star,  if  above  the 
horizon  at  all,  remain  above,  at  the  north  or  the  south 
pole?  (See  Fig.  15.) 

2.  At  the  equator?     (Fig.  16.) 

3.  During  what  portion  of  the  twenty-four  hours 
does  a  star  at  o,  Fig.  1 7,  remain  above  the  horizon  ? 


Fig.  16.    Daily  Motion  of  Heavens  as  seen  at  the  Equator. 

a  star  at  a,  over  the  equator?   at  s,  north  of  the  equa- 
tor? at  w,  south  of  the  equator? 

4.  When  the  sun  is  above  the  horizon  at  the  north 
pole,  does  he  set  during  the  twenty-four  hours?    (^, 

Fig.  15.) 

5.  Is  the  sun  ever  more  or  less  than  twelve  hours 
above   the   horizon   at   the   equator,  whether  he   be 
directly  over  the  equator,  or  north  or  south  of  it? 
(j,  0,  w,  Fig.  1 6.) 

6.  How  does   day  compare  with  night  in  length 


38 


THE  EARTH* S  DAILY  MOTION. 


when  the  sun  is  at  a,  Fig.  17?   at  s?   at  w?     (Com- 
pare with  Fig.  24.) 

7.  Suppose  the  sun  ever  appeared  as  far  north  as  o, 
Fig.  1 7,  what  portion  of  the  twenty-four  hours  would 
be  day  and  night  respectively  ? 

71.  The  Distance  of  the  North  Star  above  the 
Horizon  at  any  Place,  measures  its  North  Latitude. 


Fig.  17.    Daily  Motion  of  Heavens  as  seen  at  Latitude  about  40°. 

—  If  we  are  at  the  equator,  we  see  the  north  star  in 
the  horizon,  showing  that  our  latitude  is  o.  If  we  are 
at  the  north  pole,  we  see  the  north  star  in  the  zenith, 
or  90°  above  the  horizon,  showing  that  our  latitude  is 
90°.  If  we  are  at  latitude  40°  north  (X,  Fig.  17)  we 
see  the  north  star  P  40°  above  the  horizon,  etc. 


THE  EARTH'S    YEARLY  MOTION.  39 


EXERCISES. 

1.  What  represents  the  circle  of  perpetual  apparition  in  Fig. 
15?     Fig.  16?     Fig.  17? 

2.  If  the  earth  turned  on  its  axis  from  east  to  west,  in  what 
direction  would  the  heavens  seem  to  move? 

3.  Would  there  be  anything  of  importance  to  distinguish  the 
north  star  from  the  rest  of  the  stars  if  the  earth  did  not  rotate  ? 
Would  any  of  the  stars  appear  to  move  ? 

4.  How  far  south  must  we  go  in  order  to  see  the  south  pole 
of  the  heavens? 

5.  The  crew  of  a  ship  see  the  north  star  above  the  horizon, 
one-fifth  of  the  distance  from  the  horizon  to  the  zenith;   in  what 
latitude  are  they?     (§71.) 

6.  At  a  time  when  the  sun  is  known  to  be  over  the  equator, 
a  ship's  crew  see  it,  at  noon,  10°  south  of  the  zenith;   in  what 
latitude  are  they? 

7.  Then,  may  latitude  be  determined  from  the  sun,  as  well  as 
from  the  north  star? 


VIII.     THE    EARTH'S   YEARLY   MOTION. 

72.  What  makes  the  Earth  move  around  the  Sun? 

—  If  a  stone  be  attached  to  an  elastic  cord  and  swung 
around  the  hand,  not  only  will  the  earth's  revolution 
around  the  sun  be  illustrated,  but  also  the  two  forces 
which  produce  the  revolution.  The  force  exerted  by 
the  hand  tends  to  throw  the  stone  in  a  direction  from 
the  hand ;  and  if  that  force  should  cease  the  elastic 
cord  would  pull  the  stone  towards  the  hand.  The 
cord  prevents  the  stone  from  moving  from  the  hand, 
and  if  the  cord  should  break  the  stone  would  fly  off  in 


40  THE  EARTH'S   YEARLY  MOTION. 

a  straight  line  in  the  direction  in  which  it  happened  to 
be  moving  when  the  cord  parted. 

If,  for  example,  the  cord  should  part  when  the  stone 
reached  A,  Fig.  18,  the  latter  would  fly  off  in  the  line 
AB ;  at  C  it  would  take  the  direction  CD,  etc.*  But 
so  long  as  the  cord  remains  unbroken  —  since  the 


D 


Fig.  18.    Centripetal  and  Centrifugal  Forces. 

stone  cannot  move  either  towards  or  from  the  hand  — 
it  must  take  a  direction  between,  or  in  a  curve  around 
the  hand. 

In  like  manner,  the  force  which  was  first  communi- 
cated to  the  earth  tends  to  cause  it  to  move  onward  in 
a  straight  line,  while  the  sun's  attraction  tends  to  draw 
it  to  the  sun;  but  the  two  opposite  forces  are  so 

*  The  lines  AB  and  CD  are  tangents  to  the  circle  ACE. 


THE  EARTH'S   YEARLY  MOTION.  41 

adjusted  that  it  moves  in  a  nearly  circular  pathway 
around  the  sun,  which  is  called  its  orbit. 

73.  Centrifugal  and  Centripetal  Forces.  —  The  force 
which  tends  to  move  a  body  in  a  straight  line  is  called, 
for  want  of  a  better  term,  centrifugal ' ;  that  which  tends 
to  draw  it  from  this  straight  line  into  a  curve  is  called 
centripetal. 

EXERCISES. 

1 .  Which  of  these  forces  prevents  the  stone  from  being  drawn 
to  the  hand? 

2.  Which  prevents  the  stone  from  flying  from  the  hand? 

3.  Which  prevents  the  earth  from  falling  to  the  sun? 

4.  Which  prevents  the  earth  from  flying  off  into  space? 

74.  Form  of  the  Earth's  Orbit. — If  the  two  forces, 
centrifugal  and  centripetal,  were  exactly  balanced,  and 
no  disturbances  were  made  by  the  attraction  of  other 
planets,  the  earth's  orbit  would  be  a  perfect  circle ; 
but  such  is  not  the  case ;   its  real  form  is  that  of  an 
oval,  or  ellipse,  with  the  sun  in  one  focus. 

75.  Perihelion  and  Aphelion.  —  The   earth's  orbit 
being  an  ellipse,  our  distance   from   the   sun  varies 
slightly  at  different  times.     When  the  earth  is  nearest 
the  sun  it  is  said  to  be  in  perihelion  ;  when  most  dis- 
tant, in  aphelion.     (§  41.) 

76.  Both  Daily  and  Yearly  Motions  are  in  the 
Same  Direction ;  viz.,  from  west  to  east.    The  relation 
of  the  two  motions  may  be  fixed  in  the  memory  by 
associating  them  with  those  of  a  rolling  ball  or  a  car- 
riage wheel,  which  may  be  said  to  rotate  in  the  same 
direction  in  which  it  advances. 


42  THE  EARTH'S    YEARLY  MOTION. 

77.  Principal  Effects  of  the  Earth's  Revolution 
around  the  Sun.  —  i .  The  apparent  yearly  revolution 
of  the  sun  around  the  earth,  through  the  twelve  Signs 
of  the  Zodiac. 

2.  The  Change  of  Seasons.  This  is  a  combined 
result  of  the  yearly  motion  and  the  inclination  and 
unchanging  direction  of  the  earth's  axis. 

HOW  WE  KNOW  THAT  THE  EARTH  REVOLVES  AROUND 
THE  SUN. 

78.  Cause  of  the  Sun's  Apparent  Yearly  Motion.  — 

As  the  earth's  real  motion  upon  its  axis  causes  the 
whole  heavens  to  seem  to  move  around  the  earth  once 
a  day,  so  the  earth's  real  motion  around  the  sun  causes 
the  sun  to  seem  to  move  around  the  earth  once  a  year. 

79.  f  In  what  the  Sun's  Apparent  Yearly  Motion 
consists.  —  The  apparent  daily  revolution  of  the  sun 
around  the  earth  has  nothing  to  do  with  its  apparent 
yearly  revolution.     The  former  is  an  apparent  move- 
ment of  the  sun  in  company  with  the  whole  heavens, 
while  the  latter  consists  in  its  apparent  changes  of  posi- 
tion among  the  stars. 

The  stars  on  account  of  their  immense  distances 
seem  as  immovably  fixed  in  the  immense  hollow  sphere 
that  surrounds  us  as  if  they  were  silver  nails  in  a  blue 
ceiling ;  and  they  appear  to  turn  with  that  hollow 
sphere  once  a  day,  as  the  nails  would  move  with  the 
ceiling  if  the  latter  should  perform  a  rotation. 
•  But  the  sun,  although  in  reality  a  star,  does  not 
appear  thus  fixed  on  account  of  its  comparative  near- 


THE  EARTH'S   YEARLY  MOTION.  43 

ness  to  us.  As  you  ride  swiftly  along  in  a  railway  car, 
you  notice  that  objects  in  the  landscape  appear  to 
move  swiftly  or  slowly  past  you,  according  to  their 
comparative  nearness  or  distance ;  distant  mountains 
appear  motionless,  like  the  fixed  stars.  So,  if  we  could 
see  the  sun  and  stars  together  in  the  daytime  we  should 
see  it  slowly  creeping  past  them  from  west  to  east,  as 
we  see  from  our  car  window  a  tree  or  a  house  creeping 
past  the  distant  mountains.  If  it  appears  beside  the 
star  a,  Fig.  21,  at  sunset  to-day,  it  will  appear  at  b,  a 
little  east  of  (above)  that  star,  at  sunset  to-morrow, 
when  the  star  a  will  be  just  below  the  horizon.  The 
next  day  at  sunset  the  sun  will  appear  still  farther  east, 
so  that  the  point  b  will  then  be  below  the  horizon,  and 
so  on,  until,  in  365^  days,  the  sun  will  appear  to  have 
made  an  entire  circuit  around  the  heavens,  and  to 
have  returned  to  its  starting  point  beside  a. 

80.  f  We  may  observe  the  Sun's  Apparent  Motion 
among  the  Stars  as  accurately  as  if  they  were  visible 
in  the  Daytime.  —  i .  If  we  observe  what  stars  are  just 
above  the  western  horizon  as  soon  after  sunset  as  they 
become  visible  (the  uppermost  stars  in  Fig.  21  for 
example),  we  shall  find  at  the  same  time  to-morrow 
that  these  stars  have  descended  somewhat,  which  will 
show  that  the  sun  has  approached  them ;  that  is,  that 
he  has  moved  a  little  eastward. 

2.  Since  the  sun  is  on  the  meridian  upon  the  other 
side  of  the  earth  at  midnight,  certain  stars  on  our 
meridian  must  be  exactly  opposite  the  sun;  and,  as 
different  stars  appear  on  our  meridian  at  midnight 


44 


THE  EARTH'S    YEARLY  MOTION. 


night  after  night,  the  sun  must  be  opposite  different 
stars  at  different  times. 

For  example,  when  the  earth  is  at  a,  Fig.  19,  we  see 
the  stars  at  C  on  the  meridian  at  midnight,  and  we 
know  that  the  sun  is  on  the  other  side  of  the  earth, 


Fig.  19.     The  Earth's  Real,  and  the  Sun's  Apparent 
Yearly  Revolution. 

opposite  these  stars,  appearing  to  observers  upon  the 
opposite  side  of  the  earth  in  that  part  of  the  heavens 
denoted  by  A. 

Three  months  afterward,  when  the  earth  has  moved 
to  b,  we  shall  see  the  stars  at  D  on  the  meridian  at 
midnight,  and  shall  know  that  the  sun  is  opposite 
them. 


THE  EARTH'S    YEARLY  MOTION.  45 


EXERCISES. 

1.  To  what  point  will  the  earth  have  moved  three  months 
later? 

2.  What  stars  shall  we  then  see  on  the  meridian  at  midnight? 

3.  Among  what  stars  would  the  sun  seem  to  be  at  this  time, 
if  we  could  see  the  stars  by  daylight  ? 

4.  As  the  earth  moves  from  c,  to  d,  the  sun  seems  at  the  same 
time  to  move  past  what  stars? 

5.  Would  the  sun  seem  to  make  this  movement  if  the  earth 
remained  motionless? 

6.  If  the  sun  seems  to  move  entirely  around  the  heavens  in 
a  year,  through  what  part  of  the  circle  does  he  seem  to  move 
in  a  day?  —  A  us.   Nearly  one  degree. 

8 1 .  Other  Heavenly  Bodies  move  among  the  Stars. 

—  The  moon  and  planets  also  change  their  positions 
among  the  stars  from  day  to  day,  moving  generally  in 
the  same  direction  in  which  the  sun  moves ;  viz.,  from 
west  to  east.  But  here  a  most  important  distinction 
must  be  made ;  the  moon  and  planets  really  move, 
while  the  sun's  motion  is  only  apparent. 

82.  The  Zodiac  is  that  great  zone,  or  belt,  of  the 
heavens  within  which  the  sun,  moon,  and  planets  are 
seen  to  move.     It  is  sixteen  degrees  in  width,  eight 
degrees  each  side  of  the  ecliptic  (§  83).     The  stars 
within  the  zodiac  are   divided  into   twelve  constella- 
tions, from  which  the  twelve  Signs  of  the  Zodiac  are 
named.     (Appendix  IV.) 

83.  The  Ecliptic  is  the  earth's  real  yearly  path,  or 
sun's  apparent  yearly  path,  through  the  heavens.     It 
lies  along  the  middle  of  the  zodiac,  as  seen  in  Figs, 
20  and  21. 


46  THE  EARTH'S    YEARLY  MOTION. 

f  Fig.  2 1  represents  the  sun  setting,  with  the  stars 
visible,  as  they  would  be  if  it  were  not  for  the  atmos- 
phere (§  49).  The  space  within  the  two  oblique  lines 
on  either  side  of  the  sun  represents  a  portion  of  the 


Fig.  20.     Zodiac  encircling  the  Heavens. 

zodiac,  with  the  ecliptic  running  along  the  middle. 
Nearly  the  whole  of  the  sign  Cancer  (gs)  is  seen,  with 
a  portion  of  Leo  (  SI )  and  a  corner  of  Gemini  ( n  ) . 
(See  Appendix  IV.) 
On  the  2ist  of  June  we  see  the  sun  entering  the 


THE  EARTHS   YEARLY  MOTION.  47 

sign  Cancer.  When  he  sets  the  next  day,  he  will  have 
advanced  nearly  one  degree  into  Cancer  —  having 
moved  along  the  ecliptic  to  b,  as  shown  in  §  79  — 
leaving  the  star  a  below  the  horizon.  A  month  later 
he  will  have  moved  along  the  ecliptic  to  Leo  (  SI ) .  At 
sunset  at  this  time  the  bright  stars  seen  in  the  engrav- 
ing will  be  below  the  horizon,  and  those  above,  or  east 
of  them,  will  have  taken  their  place.  During  the  next 
month  the  sun  will  enter  Virgo  (*%),  the  next  sign 
east  of  Leo. 

t Solar  and  Sidereal  Day.  —  Questions:  i.  Suppose 
the  sun  and  a  certain  star,  a,  Fig.  21,  set  at  the  same 
instant  to-day ;  which  will  set  first  to-morrow  ? 

2.  What  will  be  the  difference  in  their  time  of  set- 
ting?—  Ans.   The  sun,  being  -^^  of  the  whole  circle 
around  the  heavens  east  of  the  star,  will  set  -g-J--  of  24 
hours,  or  nearly  four  minutes,  later. 

Hence,  the  time  between  sunset  and  sunset  is  about 
four  minutes  longer  than  that  between  starset  and  star- 
set.  The  former  is  called  a  solar  day,  and  the  latter  a 
sidereal  day.  Each  is  divided  into  twenty-four  equal 
parts,  called  in  one  case  solar  hours,  and  in  the  other 
sidereal  hours. 

3.  How  many  solar  hours  and  minutes  are  there  in 
a  sidereal  day?  —  Ans.    23?!.  56  min.  (nearly). 

4.  How  many  sidereal  days  in  365  solar  days?  — 
Ans.   366  (nearly). 

84.  An  Effective  Illustration  of  this  whole  subject 
may  be  made  as  follows  :  Let  the  blackboards  around 
the  schoolroom  represent  the  zodiacal  belt  around  the 
celestial  sphere.  Let  the  head  of  a  pupil  standing  in 


48 


THE  EARTH'S    YEARLY  MOTION. 


THE  EARTHS    YEARLY  MOTION.  49 

the  centre  of  the  room  represent  the  sun.  Then  let 
another  pupil,  carrying  a  globe  with  its  axis  properly 
inclined,  walk  around  the  "  sun "  to  represent  the 
earth  moving  in  its  orbit.  Let  a  third  pupil  walk  along 
by  the  blackboards  and  mark  the  points  against  which 
the  second  pupil  sees  the  "sun"  projected  from  his 
different  positions.  A  continuous  line  connecting  these 
points  will  represent  the  ecliptic  passing  along  the 
middle  of  the  zodiac.  Then  let  the  zodiacal  signs  be 
properly  placed  with  "Cancer"  and  " Capricornus  " 
over  their  respective  tropics  on  the  globe.  Let  the 
globe  rotate  once  on  its  axis  while  its  bearer  advances 
a  step  in  the  orbit  to  show  how  the  sun  seems  to  pass 
one  degree  along  the  ecliptic  in  one  day.  (See  Ap- 
pendix V.) 

t  EXERCISES. 

1.  What  distinguishes  the  constellations  of  the  zodiac  from 
the  other  constellations  in  the  sky?     (§  82.) 

2.  If  the  sun  is  exactly  on  the  meridian  at  this  moment, 
where  will  it  be  in  exactly  twenty-four  hours?     Where  will  it  be 
in  exactly  one  sidereal  day? 

3.  As  you  ride  in  the  cars,  what  objects  seem  to  move  past 
you  more   rapidly,  those  which  are  near,  or  those  which  are 
more  distant?    Then,  if  you  had  no  other  means  of  judging  of 
distance,  which  would   you   conclude  to  be  farther  off,   those 
which  seem  to  move   slowly,  or  those  which   seem   to   move 
rapidly?     What  would  you  conclude  to  be  the  distance  of  hill- 
tops which  seem  not  to  move  past  you  at  all? 

4.  The  earth  is  carrying  you  along  in  its  orbit  as  the  car 
carries  you  along  over  the  rails  (having,  at  the  same  time,  an- 
other motion  which  the  car  has  not;  viz.,  rotation);   you  see  the 
sun  and  stars  in  the  zodiac,  as  you  see  various  objects  in  the 
landscape  from  the  car  window.     The  sun  seems  to  change  its 
place  as  you  move;   the  stars  do  not.     What  may  you  conclude 
from  this  alone,  in  regard  to  their  comparative  distances? 


50      INCLINATION  OF  THE  EARTH'S  AXIS. 


IX.   THE  INCLINATION  OF  THE  EARTH'S  AXIS. 

85.  Plane  of  the  Earth's  Orbit,  or  Plane  of  the 
Ecliptic. — Suppose  two  spheres  representing  the  earth 
and  the  sun  to  be  half  immersed  in  a  smooth  sheet  of 
water,  the  former  floating  around  the  latter  in  an  ellip- 
tical orbit,  shown  by  the  dark  line  (Fig.  22).     The 
smooth  surface  of  the  water  represents  a  plane  passing 
through  the  earth's  orbit.     Now,  if  you  can  imagine 
the  water  removed  and  the  spheres  still  continuing 
their  motions  undisturbed,  the  exact  space  which  the 
surface  of  the  water  occupied  will   present  to  your 
mind  a  very  accurate  idea  of  the  plane  of  the  earth's 
orbit,  or  plane  of  the  ecliptic.     It  must  be  imagined 
as  cutting  through  the  centres  of  both  sun  and  earth, 
and  extending  to  an  indefinite  distance  beyond  the 
earth's  orbit.     To  an  observer  standing  upon  the  ball 
representing  the  earth  the  other  ball  would  seem  to 
move  around  him  in  the  surface  of  the  water ;  hence 
the  plane  of  the  earth's  orbit  is  also  the  plane  of  the 
sun's  apparent  path,  or  ecliptic.     (Appendix  VI.) 

86.  The  Earth's  Axis  is  inclined  to  the  Plane  of 
the  Ecliptic.  —  We  observe  that  the  earth's  axis,  as 
represented  in  Fig.  22,  does  not  stand  upright  in  the 
plane  of  the  ecliptic,  and  that  the  equator  is,  there- 
fore, cut  by  the  plane  in  two  points. 

The  Amount  of  the  Inclination  of  the  Earth's  Axis 
to  a  perpendicular  to  the  plane  of  the  ecliptic  is  23  J 
degrees,  or  66£  degrees  to  the  plane  itself. 


INCLINATION  OF  THE  EARTH* S  AXIS.      51 


52      INCLINATION  OF  THE  EARTH'S  AXIS. 

Let  NESW  represent  the  earth,  and  the  line  S'S' 
the  plane  of  the  ecliptic  with  its  edge  turned  exactly 
towards  us.  If  the  axis  were  perpendicular  to  the 
ecliptic,  it  would  be  represented  by  the  line  PR,  and 
TT'  would  represent  the  equator  lying  exactly  in  the 
plane,  or,  as  the  usual  expression  is,  "  coinciding  with 


Fix.  23.     Inclination  of  the  Earth's  Axis. 

it."  If,  now,  we  take  the  north  pole,  P,  and  move  it 
23!  degrees  to  the  point  N,  we  shall  have  it  in  its  true 
position.  While  we  are  doing  this  we  move  every 
other  point  in  the  whole  circumference  an  equal  dis- 
tance ;  the  point  R  moves  to  S,  and  the  points  TT'  of 
the  equator  move  to  W  and  E,  each  23^-  degrees  from 
the  plane  of  the  ecliptic. 


INCLINATION  OF  THE  EARTH'S  AXIS.      53 

87.  Relation  of  the  Tropics  to  the  Equator  and  to 
the  Plane  of  the  Ecliptic.  —  The  tropics  of  Cancer  and 
Capricorn  are  denoted  by  the  circles  on  either  side  of 
the  equator  in  Fig.  22,  and  by  the  lines  OT'  and  TF 
in  Fig.  23.     They  are  each  23^   degrees   from    the 
equator,  and  we  see  that  the  plane  of  the  ecliptic  cuts 
across  from  one  to  the  other. 

A  circle  called  the  "  Ecliptic  "  is  generally  drawn 
upon  terrestrial  globes  across  the  equator  from  tropic 
to  tropic.  A  similar  circle  is  made  by  the  surface  of 
the  water  around  the  globe  represented  in  Fig.  22, 
which  explains  the  meaning  of  the  former.  The  circle 
drawn  upon  the  globe  must  rotate  with  the  globe,  how- 
ever, whereas  it  should  be  stationary,  like  the  circle 
made  by  the  surface  of  the  water. 

88.  The  Earth's  Axis  constantly  points  in  the 
Same  Direction  during  the  Yearly  Revolution ;  viz., 
towards  the  North  Star.  —  If  it  were  not  for  this  fact 
we   should   not   always   see    the  north   star,   summer 
and  winter,  at  the  same  distance  above  the  northern 
horizon. 

This  unchanging  direction  of  the  earth's  axis  is  ex- 
hibited in  Fig.  26.  The  north  star  must  be  imagined 
at  an  immense  distance  in  the  direction  in  which  the 
various  lines  denoting  the  earth's  axis  point ;  so  that, 
although  the  lines,  being  parallel,  are  really  directed 
to  four  different  points,  yet,  like  the  parallel  lines  of  a 
railway  track,  they  seem  to  meet  in  a  single  point  in 
the  distance. 

89.  How  we  know  that  the  Earth's  Axis  is  in- 
clined to  the  Plane  of  the  Ecliptic,  —  The  fact  of  the 


54      INCLINATION  OF  THE  EARTHS  AXIS. 

inclination  is  proved,  and  its  amount  measured,  by 
the  sun's  apparent  movements  north  and  south  of  the 
equator,  treated  of  in  the  following  section. 

THE  SUN'S  DECLINATIONS,  OR  APPARENT  MOVEMENTS 
NORTH  AND  SOUTH  OF  THE  EQUATOR. 

90.  Cause  of  the  Sun's  Declinations.  —  Every  one 
is  familiar  with  the  expressions,  "  The  sun  is  crossing 
the  line";    "The  sun  is  coming  north,  and  we  shall 
soon  have  warm  weather  "  ;    "  The  sun  is  going  south, 
and  the  days  are  growing  shorter " ;  etc.     Like  the 
two  apparent  movements  of  the  sun  already  described, 
this  is  not  due  to  any  change  in  the  sun's  real  position, 
but  must  come  home  to  the  earth  itself.     The  cause  is 
threefold  :  - 

(1)  The  inclination  of  the  earth's  axis. 

(2)  The  unchanging  direction  of  the  axis. 

(3)  The  earth's  revolution  around  the  sun. 

As  a  result  of  these  three  conditions,  the  north  pole 
of  the  earth  is  sometimes  inclined  directly  towards 
the  sun,  at  which  time  the  sun  is  over  the  tropic  of 
Cancer,  23!  degrees  north  of  the  equator.  At  other 
times  the  north  pole  is  inclined  directly  from  the  sun, 
at  which  time  the  sun  is  over  the  tropic  of  Capricorn, 
23!  degrees  south  of  the  equator.  During  the  inter- 
mediate times  the  sun  must  be  somewhere  between 
these  circles,  being  directly  over  the  equator,  or 
"  crossing  the  line,"  twice  a  year. 

9 1 .  The  Sun's  Declinations  appear  in  a  Spiral  Path 
winding  around  the  Sky,  like  the  Threads  of  a  Screw. 
—  This  is  in  consequence  of  the  earth's  two  motions 


INCLINATION  OF   THE  EARTH'S  AXIS.       55 

going  on  together.  On  the  2Oth  of  March  we  see  the 
sun  rise  at  E,  Fig.  24,  describe  the  arc  through  A,  and 
set  at  C.  This  arc  is  directly  over  the  equator,  and  is, 
therefore,  the  equinoctial.  Day  and  night  are  now  of 
equal  length,  and  the  period  is  for  this  reason  styled 


Fig.  24.     Sun's  Apparent  Motion  on  Different  Days  during 
the  Year,  North  and  South  of  the  Equator. 


the  spring,  or  vernal,  equinox.  On  the  next  day  the 
sun  describes  a  circle  a  little  north  of  the  equinoctial ; 
the  next,  still  farther  north ;  and  so  on,  until  on  the 
2ist  of  June  he  has  reached  the  limit  of  his  northern 
declination.  The  circle  which  he  describes  on  this 
day,  S,  is  directly  over  the  tropic  of  Cancer,  23^  de- 
grees north  of  the  equator,  or  equinoctial.  For  a  few 


56      INCLINATION  OF  THE  EARTH'S  AXIS. 

days  he  seems  to  describe  nearly  the  same   circle, 
whence  the  name  of  the  period,  summer  solstice* 

From  the  summer  solstice  the  sun  describes  his 
circles  farther  and  farther  south  each  day,  until  on  the 
23d  of  September  he  again  describes  the  equinoctial, 
EAC.  Day  and  night  are  again  equal — the  autumnal 
equinox.  Thence  he  continues  still  southward  till  the 
2ist  of  December,  when  he  describes  the  circle  W 
over  the  tropic  of  Capricorn.  This  is  the  limit  of  his 
southern  declination,  the  winter  solstice,  from  which 
after  a  few  days  he  begins  his  return  northward. 

In  Fig.  21  the  oblique  line  at  the  left  of  the  zodiac 
represents  a  portion  of  the  equinoctial.  The  sun  is 
seen  at  his  greatest  distance  north  (the  summer  sol- 
stice), and  as  he  moves  along  the  ecliptic  toward  Si 
day  after  day,  it  is  plain  that  he  will  constantly  ap- 
proach the  equinoctial,  until  he  will  cross  it  at  the 
autumnal  equinox. 

92.  Tropics  named  from   the   Signs    Cancer  and 
Capricornus.  —  On  the  2ist  of  June,  when  the  sun  is 
over  the  tropic  of  Cancer,  he  is  also  entering  the  sign 
Cancer;  on  the  2ist  of  December,  when  he  is  over 
the  tropic  of  Capricorn,  he  is  entering  the  sign  Capri- 
cornus. 

93.  The  Effects  of  the  Sun's  Northern  and  South- 
ern Declinations :  — 

(1)  The  Change  of  Seasons. 

(2)  The    Variation    in    the   Length   of   Day   and 
Night. 

•*  Solstice  means  stationary  sun, 


INCLINATION  OF  THE  EARTH'S  AXIS.      57 


THE  CHANGE  OF  SEASONS.  —  THE  VARIATION  IN  THE 
LENGTH  OF  DAY  AND  NIGHT. 

94.  Suppose  the  Earth's  Axis  were  Perpendicular 
to  the  Plane  of  the  Ecliptic  (Fig.  25),  then  the  plane 
of  the  ecliptic  would  coincide  with  the  equator,  and 
the  sun  would,  accordingly,  always  be  seen  over  the 
equator.  His  northernmost  rays  would  always  strike 
exactly  at  the  north  pole ;  his  southernmost  rays,  at 
the  south  pole.  Those  rays  which  reach  us  would 


Fig.  25.     Axis  Perpendicular  to  Ecliptic. 

come  in  precisely  the  same  direction  every  day  through- 
out the  year,  and  there  would  be  nothing  to  produce  a 
change  of  seasons  except  the  difference  in  our  distance 
from  the  sun  at  different  points  of  the  orbit  (§  41). 
This  difference,  however,  is  so  extremely  slight  that  in 
all  probability  ordinary  observers  could  not  detect  the 
consequent  difference  of  temperature,*  and  conse- 

*  Whatever  difference  there  might  be  would  be  just  opposite  to 
that  produced  by  the  sun's  declinations,  at  least  in  the  northern 
hemisphere,  for  we  .are  nearest  the  sun  in  winter.. 


58      INCLINATION   OF  THE  EARTH'S  AXIS. 

quently  there  would  be  perpetual  winter  in  the  frigid 
zones,  perpetual  spring  in  the  temperate  zones,  and 
perpetual  summer  at  the  equator. 

Every  parallel  circle  would  be  half  the  time  in  the 
sunlight  and  half  the  time  in  the  shade,  so  that  day 
and  night  would  be  equal  throughout  the  year  at  every 


Fig.  26.     The  Change  of  Seasons. 

point  on  the  earth's  surface  —  a  perpetual  equinox  — 
except  at  the  poles,  where  the  sun  would  always  be 
seen  in  the  horizon. 

95.  The  Change  of  Seasons. — We  have  seen  (§  54) 
that  the  change  of  seasons  is  due  to  differences  in  the 
direction  of  the  sun's  rays,  which  beat  almost  directly 
upon  our  heads  in  midsummer,  and  fall  very  obliquely 
in  midwinter  Also  (§  90)  that  these  differences  of 
direction,  in  other  words  the  sun's  declinations,  are 
produced  by  the  inclination  and  unchanging  direction 


INCLINATION  OF   THE  EARTH'S  AXIS.       59 

of  the  earth's  axis,  together  with  the  earth's  yearly 
revolution  around  the  sun. 

Any  two  of  these  three  conditions  may  be  con- 
ceived to  exist  without  necessarily  producing  a  change 
of  seasons.  For  example,  we  may  imagine  the  earth's 
axis  as  always  preserving  its  present  inclination  of 
2  3i  degrees,  while  at  the  same  time  its  north  pole 
inclines  exactly  towards  the  sun  during  the  entire 
yearly  revolution.  In  this  case  the  sun  would,  of 
course,  always  be  vertical  at  the  tropic  of  Cancer, 
causing  a  perpetual  summer  in  the  northern  hemi- 
sphere, and  a  perpetual  winter  in  the  southern  hem- 
isphere. 

96.  The  Variation  in  the  Length  of  Day  and 
Night.  —  This  change  is  due  to  the  same  cause  that 
produces  the  change  of  seasons ;  for,  when  the  sun  is 
north  or  south  of  the  equator,  more  or  less  than  half 
of  each  parallel,  except  the  equator,  is  in  the  sunlight 
at  a  time,  as  may  be  seen  from  Figs.  28  and  30,  or 
from  the  right  and  left  of  Fig.  26.  At  these  times, 
therefore,  we  are  more  or  less  than  twelve  hours  in 
passing  through  the  sunlight  or  shade. 

(The  same  truth  was  shown  in  a  different  manner 
by  Fig.  17.) 

Both  summer  heat  and  winter  cold  are  thus  in- 
creased ;  for  the  sun  shines  upon  us  in  summer  not 
only  more  directly,  but  for  more  hours  at  a  time  than 
in  winter. 

Let  us  now  examine,  in  regular  order,  the  changing 
relations  which  the  earth  bears  to  the  sun  as  it  moves 
in  its  orbit. 


60      INCLINATION  OF  THE  EARTH'S  AXIS. 

97.  The  Vernal  Equinox,  2Oth  of  March.  —  The 
sun  enters  the  sign  Aries.  (See  bottom  of  Fig.  26. 
The  sun  as  seen  from  the  earth  in  this  part  of  its  orbit 
appears  in  Aries.)  Neither  pole  of  the  earth  inclines 
towards  or  from  the  sun,  but  sidewise  ;  hence  the  sun 
is  vertical  at  the  equator,  his  northernmost  and  south- 


SOUTHERN  MOST 

RAYS 

Fig.  27.    Earth  at  Vernal  Equinox. 

ernmost  rays  fall  at  the  poles,  and  day  and  night  are 
everywhere  equal.  It  is  spring  in  the  northern  and 
autumn  in  the  southern  hemisphere. 

As  the  earth  moves  on  from  the  vernal  equinox,  the 
north  pole  begins  to  lean  towards  the  sun  and  the  south 
pole  from  it ;  the  sun,  therefore,  is  vertical  farther  and 
farther  north  of  the  equator  each  day  (see  Fig.  26), 
until  — 

98.  The  Summer  Solstice,  2ist  of  June.  —  The 
sun  now  enters  Cancer.  The  north  pole  leans  exactly 
towards  the  sun,  and  the  south  pole  exactly  from  it ; 
consequently,  the  sun  is  vertical  23^  degrees  north  of 
the  equator,  and,  if  his  vertical  rays  should  leave  a 
track  as  the  earth  turns  upon  its  axis,  they  would  mark 
the  tropic  of  Cancer  upon  the  surface  (Fig.  28). 


INCLINATION  OF  THE  EARTH'S  AXIS.      61 

The  northernmost  ray  of  the  sun  falls  23^  degrees 
beyond  the  north  pole,  and  would  if  it  left  a  track 
mark  the  arctic  circle  as  the  earth  turns  upon  its  axis. 
The  southernmost  ray  falls  23^  degrees  short  of  the 
south  pole,  and  describes  the  antarctic  circle. 

No  point  within  the  arctic  circle  passes  out  of  the 
sunlight,  and  no  point  within  the  antarctic  circle  passes 
into  the  sunlight,  during  the  earth's  rotation ;  hence  a 
24-hours'  day  within  the  former,  and  a  24-hours'  night 


Fig.  28.     Earth  at  Summer  Solstice. 

within  the  latter.  The  long  twilight,  however,  practi- 
cally shortens  the  night  very  much  in  the  antarctic 
circle,  excepting  in  a  small  space  around  the  pole. 
(See  p.  25,  note  at  bottom.) 

More  than  half  of  each  parallel  circle  in  the  north- 
ern hemisphere  is  in  the  sunlight  at  a  time,  and  less 
than  half  of  each  parallel  circle  in  the  southern  hemi- 
sphere ;  hence  the  days  are  longer  than  the  nights  in 
the  former,  and  shorter  than  the  nights  in  the  latter. 
It  is  summer  in  the  northern  and  winter  in  the  south- 
ern hemisphere. 


62      INCLINATION  OF  THE  EARTH'S  AXIS. 

From  the  summer  solstice,  the  poles  incline  less  and 
less  towards  and  from  the  sun,  and  the  sun's  vertical 
rays  fall  farther  and  farther  south,  until  — 

99.  The  Autumnal  Equinox,  23 d  of  September. — 
QUESTIONS  :  — 

1 .  What  season  is  it  in  the  northern  hemisphere  ? 
In  the  southern? 

2.  How  do  the  poles  lean  with  reference  to  the 
sun?     (Fig.  29.) 

3.  Where  do  the  northernmost  and  southernmost 


RAYS 
Fig.  29.     Earth  at  Autumnal  Equinox. 

rays  of  the  sun  fall  ?     Then  on  what  circle  of  the  earth 
do  the  vertical  rays  fall  ? 

4.   What  is  the  length  of  day  and  night? 

100.    The  Winter   Solstice,  2ist  of  December. — 
QUESTIONS  :  — 

1 .  What  season  in  each  hemisphere  ? 

2.  At  what  circle  of  the  earth  is  the  sun  vertical? 

3.  Which  pole  leans  exactly  towards  the  sun? 

4.  Where  do  the  northernmost  and  southernmost 
rays  fall? 


INCLINATION  OF   THE  EARTH'S  AXIS.      63 

5.  In  which  zone  is  there  a  24-hours'  day?     In 
which  a  24-hours'  night? 

6.  How  does  the  day  compare  with  the  night  in 
each  hemisphere? 

ADDITIONAL  OBSERVATIONS. 

1 01.    Day  and  Night  at  the  Poles  are  each  six 

months  in  length.     From  March  2Oth  to  September 

NORTH  ERNM  OS  T 
RAYS 


SOUTHERNMOST 
RAYS 


Fig.  30.     Earth  at  Winter  Solstice. 

23d  the  north  pole  remains  constantly  in  the  sunlight, 
and  the  south  pole  in  the  shade.  From  September 
23d  to  March  2Oth  the  conditions  are  reversed. 

We  arrive  at  the  same  result  by  reflecting  that  the 
poles  are  not  affected  by  the  earth's  daily  motion,  and 
that  if  it  were  not  for  this  motion  the  day  and  night 
would  be  six  months  each  throughout  the  year  over 
the  whole  earth. 

Within  the  frigid  zones,  day  and  night  each  vary  all 
the  way  from  six  months  at  the  poles  to  twenty-four 
hours  at  the  polar  circles. 


64      INCLINATION  OF  THE  EARTH'S  AXIS. 

102.  Seasons  at  the  Equator. — The  sun  crosses 
the  equator  and  departs  to  its  greatest  distance  from 
the  equator  twice  during  the  year.     There  are,  there- 
fore, two  summers  and  two  winters  annually  at  the 
equator,  although  "winter"  there  must,  of  course,  be 
much  warmer  than  our  warmest  summer.* 

103.  The  Full  Effects  of  the  Various  Changes  in 
the  Direction  of  the  Sun's  Rays  are  not  felt  at  once. 

—  Although  the  most  direct  rays  fall  at  noon,  the 
warmest  part  of  the  day  is  usually  two  or  three  hours 
later.  So,  although  the  hottest  rays  fall  at  the  sum- 
mer solstice  yet  our  warmest  weather  does  not  come 
until  some  time  afterwards.  We  continue  to  receive 
more  heat  during  the  days  following  than  we  lose 
during  the  nights.  Thus  the  great  heat  of  a  July  or 
August  day  is  not  produced  entirely  by  the  sun  of  that 
day,  but  is  an  accumulation  of  the  heat  of  the  several 
preceding  weeks.  For  a  like  reason  we  do  not  experi- 
ence the  greatest  cold  at  the  winter  solstice.  We 
continue  to  lose  more  heat  during  the  night  than  we 
receive  during  the  day,  and  the  maximum  of  cold  does 
not  arrive  until  some  time  in  January. 

EXERCISES. 

1.  Would  there  be  any  tropics  or  polar  circles  if  the  earth's 
axis  were  not  inclined  from  a  perpendicular  to  the  ecliptic? 

2.  Where  would  the  tropics  be  if  the  axis  were  inclined  45°? 
Where  would  the  polar  circles  be? 

*  The  only  seasons  practically  known  in  tropical  climates  are  the 
"  wet "  and  the  "  dry." 


INCLINATION  OF  THE  EARTH'S  AXIS.      65 

3.  How  would  the  extremes  of  heat  and  cold  compare  with 
those  we  experience? 

4.  How  much  should  the  axis  be  inclined  to  bring  the  tropic 
of  Cancer  to  New  York? 

5.  How  much  should  the  axis  be  inclined  to  bring  the  arctic 
circle  to  New  York  ? 

6.  If  the  axis  were  thus  inclined,  how  long  would  be  the  day 
and  the  night  at  the  summer  solstice  at  New  York?     Where 
would  the  sun  be  seen  at  the  winter  solstice? 


66  EXERCISES  FOR  REVIEW. 


EXERCISES   FOR   REVIEW. 

1.  Of  what  is  the  earth  a  part? 

2.  How  large  a  part? 

•    3.  Prove  that  it  is  spherical. 

4.  What  made  it  so? 

5.  Prove  that  it  is  spheroidal. 

6.  What  made  it  so  ? 

7.  What  is  its  diameter? 

8.  Its  circumference? 

9.  How  many  square  miles  in  its  surface? 

10.  How  much  is  it  flattened  at  its  poles? 

11.  What  fixes  the  position  of  its  equator  and  poles? 

12.  How  many  different  points  upon  its  surface  are  in  the 
same  latitude? 

13.  In  the  same  longitude? 

14.  In  the  same  latitude  and  longitude? 

15.  What  is  the  prime  meridian? 

1 6.  What  may  be  called  the  prime  parallel? 

17.  Which  is  the  longer,  a  degree  of  the  parallel  passing 
through  London,  or  of  that  passing  through  Washington? 

1 8.  What  zones  are  not  belts? 

19.  Give  the  breadth  of  each  zone  in  degrees. 

20.  What  circles  separate  the  zones,  and  what  fixes  the  posi- 
tion of  these  circles? 

21.  How  would  the  sky  appear  by  day  if  it  were  not  for 
the  air? 

22.  Why  is  it  not  dark  the  moment  the  sun  has  set? 

23.  Why  is  it  not  as  light  and  warm  at  sunrise  as  at  noon? 

24.  Describe  the  earth's  motions. 

25.  Why  do  they  not  cease? 

26.  Prove  that  it  rotates. 

27.  Effects  of  its  rotation. 

28.  Which  seems  to  rotate,  the  earth  or  the  starry  sphere? 


EXERCISES  FOR  REVIEW.  67 

29.  Would  this  be  the  appearance  to  a  spectator  in  space? 

30.  What  prevents  the  earth  from  flying  off  into  space? 

31.  From  falling  to  the  sun? 

32.  What  is  the  form  of  its  orbit? 

33.  Define  perihelion  and  aphelion. 

34.  What  are  the  effects  of  its  yearly  motion? 

35.  If  the  sun  were  visible  at  the  same  time  with  the  stars, 
would  it  always  appear  in  the  same  place  among  them? 

36.  How  much  would  it  appear  to  move  in  one  day? 

37.  In  what  direction? 

38.  Along  what  line? 

39.  Through  what  belt  of  the  starry  heavens? 

40.  What  is  the  cause  of  this  apparent  motion? 

41.  Why  is  a  picture  of  a  ram  placed  upon  the  Almanac  page 
for  March? 

42.  What  is  the  name  of  the  plane  cutting  through  the  centre 
of  the  earth  and  through  the  ecliptic? 

43.  Is  the  earth's  axis  perpendicular  to  this  plane? 

44.  What  would  be  the  results  if  it  were  so? 

45.  What  is  its  true  attitude  in  the  plane? 

46.  When  does  the  north  pole  lean  exactly  towards  the  sun? 

47.  Upon  which  circle  of  the  earth  do  his  vertical  rays  then 
fall? 

48.  Is  the  sun  then  high  or  low  in  the  heavens  to  us  at  noon  ? 

49.  How  does  day  compare  with  night  in  length? 

50.  What,  then,  is  the  season  at  this  time? 

51.  When  does  the  north  pole  lean  exactly  from  the  sun? 
(Repeat  Questions  47,  48,  49,  50.) 

52.  When  do  the  poles  lean  neither  towards  nor  from  the  sun? 
{Repeat  Questions  47,  48,  49,  50.) 

53.  WThat  is  the  length  of  day  and  night  at  the  poles? 

54.  Of  the  longest  day  and  night  at  the  polar  circles? 

55.  At  the  equator? 


APPENDIX. 


I.  (§  40,  p.  1 6).     The  Exact  Polar  Diameter  of  the  Earth 

is  7,899.58  miles,  while  the  equatorial  diameter  is  26.48  miles 
greater,  or  7,926.59  miles. 

Multiplying  these  numbers  by  3.1416,  we  have  the  circumfer- 
ence of  a  meridian  circle,  or  polar  circumference,  24,817  miles 
and  the  equatorial  circumference,  24,902  miles. 

II.  (§  42,  p.  16).     The  Moon's  Distance  from  the  Earth 
varies  during  the  month,  the  greatest  distance  {Apogee)  being 
about  252,000  miles;    and  the  least   {Perigee),  about  226,000 
miles.     Its  mean  distance  is,  therefore,  about  239,000  miles. 

For  the  sake  of  comparing  the  earth's  magnitude  with  that 
of  other  heavenly  bodies,  and  with  space,  other  distances  and 
magnitudes  are  annexed. 

The  Distances  of  the  Other  Known  Planets  from  the 
sun  vary  from  about  one-third  to  thirty  times  that  of  the  earth. 

Ex. — About  how  many  miles  irom  the  sun  is  the  nearest 
planet?  The  most  distant  planet? 

The  Distances  of  the  Fixed  Stars  are  so  great  that  they 
are  utterly  beyond  our  comprehension.  The  very  nearest  of  them 
is  about  200,000  times  more  distant  from  us  than  we  are  from 
the  sun.  But  even  this  vast  distance  is  small  compared  with 
that  of  the  great  multitude  of  the  stars. 

The  Sun's  Diameter  is  860,000  miles,  or  nearly  108  times 
as  great  as  that  of  the  earth.  Therefore,  as  spheres  are  to  one 
another  as  the  cubes  of  their  diameters,  the  sun  must  be  a  body 
more  than  1,250,000  (108  X  108  X  108)  times  as  large  as  the 
earth. 


70 


APPENDIX. 


The  Moon's  Diameter  is  2,162.5  miles>  °r  a  little  more  than 
one-fourth  that  of  the  earth. 

The  Diameters  of  the  Other  Known  Planets  vary  from 
a  little  less  than  one-half  to  more  than  eleven  times  that  of  the 
earth. 

Densities  of  the  Other  Heavenly  Bodies.  —  The  sun's 
density  is  ij;  that  of  the  moon  is  3^;  densities  of  the  other 
planets  vary  from  I  to  7. 

Density  of  the  Earth.  —  The  earth  weighs  about  5^  times 
as  much  as  it  would  weigh  if  composed  entirely  of  water.  We 
say,  therefore,  that  its  density  is  5^. 

III.  (§  65,  p.  31).  fFoucault's  Experiment  proving  the 
Earth's  Rotation.  —  Attach  a  pendulum  to  a  large  globe  so 

that  the  point  of  sus- 
pension shall  be  over 
its  pole;  let  the  pen- 
dulum end  in  a  sharp 
point  which  will  make 
a  scratch  upon  the 
globe  at  each  vibra- 
tion; let  the  pendu- 
lum swing,  and  slowly 
rotate  the  globe  under 
it.  You  will  observe 
that,  notwithstanding 
the  rotation,  the  pen- 
dulum will  constantly 
swing  towards  the 
same  two  points  in 
the  room;  that  is,  in 
the  same  plane.  The 

Fig.  31.    Proof  of  the  Earth's  Rotation.       consequence    will   be 

a   star-shaped    figure 

scratched  upon  the  globe  by  the  pendulum  point,  which  will 
make  a  different  line  at  each  vibration.  A  similar  experiment 
has  been  tried  upon  the  earth  itself,  with  a  like  result.  At  the 


APPENDIX.  71 

equator,  where  the  relation  between  the  plane  of  vibration  and 
the  earth's  surface  is  not  changed  by  the  rotation,  the  pendulum 
marks  only  one  line;  but  the  nearer  it  is  to  the  pole,  the  nearer 
the  figure  which  it  describes  approaches  the  star-shaped  .figure 
represented  in  the  engraving,  which  could  not  be  the  case  if 
the  earth  did  not  rotate. 

IV.  (§  82,  p.  45).    t  The  Signs  of  the  Zodiac,  with  their 
Symbols,  and  the  months  in  which  the  sun  appears  in  each 
respectively. 

1.  Aries,  the  Ram,  T  March. 

2.  Taurus,  the  Bull,  &  April. 

3.  Gemini,  the  Twins,  EE  May. 

4.  Cancer,  the  Crab,  225  June. 

5.  Leo,  the  Lion,  ft,  Juty- 

6.  Virgo,  the  Virgin,  Wjj  August. 

7.  Libra,  the  Balance,  ^=.  September. 

8.  Scorpio,  the  Scorpion,  ir\,  October. 

9.  Sagittarius,  the  Archer,  f  November. 

10.  Capricornus,  the  Goat,  VJ          December. 

11.  Aquarius,  the  Waterbearer,          %£          January. 

12.  Pisces,  the  Fishes,  X  February. 

V.  (§  84,  p.  49).     A  Field  Experiment.  —  Select  a  tree  in 
a  broad,  open  field  to  represent  the  sun,  and  station  yourself  at 
a  little  distance  from  it  to  represent  the  earth.    Now,  as  the  stars 
are  inconceivably  more  distant  than  the  sun,  they  must  be  repre- 
sented by  comparatively  distant  objects,  as,  for  example,  those  in 
the  horizon.     Suppose,  therefore,  the   tree-tops,  church-spires, 
hills,  etc.,  in  the  horizon  to  be  stars  in  the  zodiac  surrounding 
the  sun  and  earth,  like  the  circle  in  Fig.  19,  p.  44. 

Now  in  the  first  place  imitate  the  daily  motion  of  the  earth 
alone  by  turning  slowly  on  your  heels  without  moving  from  your 
place.  All  objects  in  sight  seem  to  revolve  around  you  in  the 
direction  opposite  to  that  in  which  you  are  turning,  and  not 
only  this,  but  all  seem  to  perform  their  revolutions  in  the  same 
time ;  the  objects  in  the  horizon  seem  to  describe  their  great 


72  APPENDIX. 

circles  as  quickly  as  the  tree  describes  its  small  circle.  More- 
over, you  always  see  the  tree  against  the  same  point  in  the  hori- 
zon. From  this  you  infer  that,  if  the  earth  only  rotated  on  its 
axis  without  moving  from  its  place,  the  sun  and  stars  would  per- 
form their  apparent  daily  revolutions  around  the  earth  in  pre- 
cisely the  same  time,  and  that  the  sun  would  always  be  seen 
among  the  same  stars. 

Now  imitate  the  yearly  motion  taking  place  alone,  by  moving 
in  a  circle  around  the  tree  without  turning  on  your  heels;  that 
is,  always  facing  in  the  same  direction,  as,  for  example,  south  or 
east. 

Ah !  now  a  great  difference  is  seen.  The  tree  seems  to  re- 
volve around  you  in  the  same  direction  in  which  you  revolve 
around  the  tree,  only  at  the  opposite  point  in  the  circle,  and  if 
you  watch  it  against  the  horizon  you  will  see  it  moving  past  the 
tree-tops,  church-spires,  etc.,  completing  its  apparent  revolution 
in  the  same  time  that  you  complete  your  real  revolution.  Ob- 
serve also  that  it  appears  on  one  side  of  you,  passes  in  front,  and 
disappears  on  the  other  side,  while  you  are  performing  half 
your  revolution,  and  remains  out  of  sight  during  the  other  half. 
These  appearances  teach  you  that  if  the  earth  performed  its 
revolution  around  the  sun  without  rotating  on  its  axis,  the  sun 
would  rise,  perform  a  six  months'  journey  through  the  constella- 
tions, and  then  disappear  for  the  remaining  six  months  of  the 
year.  You  notice  also  that  the  tree-tops,  etc.,  in  the  horizon  do 
not  appear  to  change  their  positions  in  the  least  perceptible 
degree  during  your  revolution  around  the  tree,  but  that  you  see 
them  in  the  same  direction  from  all  sides  of  your  orbit.  This 
illustrates  to  you  the  significance  of  the  word  fixed  as  applied 
to  the  stars,  which,  were  it  not  for  the  daily  rotation  of  the 
earth,  would  always  remain  fixed  in  the  same  points  of  the  sky, 
as  far  as  ordinary  vision  could  determine.  A  nice  instrument 
would  enable  you  to  distinguish  a  slight  parallax,  or  change  of 
position,  in  some  of  the  objects  in  the  horizon  as  viewed  from 
opposite  points  of  your  orbit  around  the  tree;  but  a  much  more 
delicate  instrument  would  be  required  to  detect  the  parallax  of 
the  stars  as  seen  from  opposite  points  of  the  earth's  orbit. 


APPENDIX.  73 

Having  imitated  the  daily  and  yearly  motions  separately,  now 
imitate  them  together,  as  the  earth  performs  them.  Of  course, 
the  two  classes  of  effects  will  be  combined,  and  will  correspond 
exactly  with  those  which  you  observe  in  the  heavens.  Every 
time  you  turn  round  to  the  tree  (sun}  you  find  it  has  made  a 
little  advance  in  the  horizon  (ecliptic),  until  it  has  described  the 
whole  circle. 

VI.  (§  85,  p.  50).  f  Meaning  of  "  Ecliptic."  —The  moon 
revolves  around  the  earth  in  an  orbit  which  crosses  the  plane  of 
the  ecliptic  at  a  small  angle,  so  that  it  is  half  the  time  on  one 
side,  and  the  other  half  on  the  other  side  of  this  plane.  The 
smallest  ball  in  the  engraving  (Fig.  22)  represents  the  moon 
thus  revolving  around  the  earth  and  crossing  the  plane  of  the 
ecliptic  in  two  points  (nodes).  Now,  no  eclipse,  either  of  the  sun 
or  moon,  can  take  place  excepting  when  the  moon  is  crossing 
the  plane,  as  is  evident  from  the  figure.  Hence,  the  plane  of  the 
earth's  orbit  takes  its  other  name  — plane  of  the  ecliptic  (or 
eclipses}. 


THE  ASTRONOMICAL  LANTERN. 


THE  object  of  the  Astronomical   Lantern  is  to 
facilitate  the  study  of  stellar  astronom}'.    It  is  in 
tended  for  beginners,   for  astronomical  classes  in 
high  schools  or  private  schools,  and,  in  fact,  for  all 
who  desire  to  become  acquainted  with  the  constel 
lations. 

The  difficulty  hitherto  experienced  in  this  study, 
and  which  is  obviated  by  the  use  of  the  Lantern, 
is  this  :  In  order  to  study  the  starry  heavens,  it  has 
been  necessary  to  use  an  astronomical  atlas,  or  a 
celestial  globe.  These  must  be  examined  in  the 
house,  by  the  light  of  a  lamp.  The  observer,  having 
found  his  constellation  on  the  atlas,  goes  out  to  look 
for  it  in  the  sky.  But,  by  the  time  he  gets  out  of 
doors,  he  has  forgotten  how  it  looked  on  the  atlas. 
And  when  he  has  found  it  in  the  sky,  he  has  for- 
gotten how  it  looked  there,  before  he  gets  back  to 
his  atlas  or  globe.  All  who  have  studied  the  con- 
stellations have  met  with  this  difficulty. 

Now,  the  Astronomical  Lantern  makes  the  study 
of  the  stars  perfectly  simple  and  easy.  It  is  con- 
structed like  a  dark-lantern,  closed  on  three  sides, 
and  on  the  fourth  provided  with  a  ground  glass,  in 
front  of  which  maps  can  be  inserted.  On  each  of 
these  maps,  which  are  semi-transparent,  is  repre- 
sented a  consteUVjon,  the  places  of  the  stars  being 


indicated  by  perforations,  through  which  the  light 
shines.  The  largest  perforations  are  for  the  stars 
of  the  first  magnitude,  and  the  smaller,  in  due  pro- 
portion, for  the  lesser  stars.  The  student,  therefore, 
wishing  to  observe  any  particular  constellation  or 
cluster,  has  only  to  light  a  candle  within  the  Lan- 
tern, insert  the  appropriate  slide,  and  go  out  into 
the  night.  Holding  up  the  Lantern  in  one  hand,  he 
can  compare  the  constellation  as  it  appears  on  the 
Lantern  with  that  in  the  sky,  until  he  becomes  per- 
fectly familiar  with  the  latter. 

It  is  easy  to  see  how  much  the  use  of  such  a 
Lantern  facilitates  the  whole  study.  In  fact,  we 
think  that  henceforth  no  one  wishing  to  become 
acquainted  with  the  heavens  can  afford  to  dispense 
with  it.  The  increased  ease  of  the  study  will  prob- 
ably also  enlarge  the  number  of  students  in  this 
interesting  department  of  science. 

To  use  the  Lantern,  it  is  necessary  to  see  what 
constellations  are  favorably  situated  for  observation 
at  the  time  ;  which  can  be  done  by  the  help  of  Dr. 
Clarke's  manual,  "How  to  Find  the  Stars,"  which 
accompanies  every  Lantern  sold. 

The  card-slides  accompanying  the  Lantern  are 
seventeen  in  number,  and  contain  all  the  constella- 
tions visible  to  an  observer  in  the  North  Temperate 
Zone.  Other  slides  may  easily  be  added  as  required. 
In  these  maps  of  the  constellations  the  nain»3  and 
the  designations  of  the  stars  are  retained,  but  the 


8 


figures  of  bears,  bulls,  unicorns,  sheep,  virgins, 
dragons,  lions,  and  the  like,  which  have  so  long 
disfigured  the  celestial  globe,  are  omitted.  Instead 
of  these  confusing  figures,  few  of  which  bear  any 
resemblance  to  the  constellations,  we  have  substi- 
tuted dotted  lines,  tying  together  in  simple  diagrams 
the  chief  stars  in  each  cluster.  Experience  shows 
that  by  these  diagrams  the  separate  constellations 
are  much  more  easily  recognized  and  remembered 
than  by  the  traditional  pictures  of  animals,  mon- 
sters, and  men,  which  have  hitherto  crowded  the 
starry  atlas.  By  these  connecting  lines,  too,  the 
principal  stars  in  each  group  are  easily  found  and 
associated  in  the  memory. 

In  preparing  these  maps,  we  have  followed  the 
' ;  Uranometria  Nova "  of  Argelander.  This  atlas 
was  selected  because  of  its  reputation  for  accuracy, 
and  because  the  scale  by  which  it  is  drawn  was  best 
adapted  to  the  size  of  the  slides.  At  the  top  of  the 
map  are  given  the  names  of  the  constellations  which 
it  contains.  At  the  bottom  is  given  their  position  in 
the  heavens  at  such  time  of  the  year  as  is  suitable 
for  observation.  The  stars  are  lettered  with  their 
proper  symbol.  Double  stars  are  indicated  by  a  D. 
The  nebulae  are  shown  by  means  of  a  group  of 
minute  dots,  and  star-clusters  in  a  similar  way.  On 
each  map  there  is  also  a  list  of  the  telescopic  objects 
which  are  to  be  found  in  the  constellations  represented 
upon  it, — those,  at  least,  which  are  suitable  for  small 


telescopes.  In  this  way  the  Lantern  may  be  of  great 
use  to  observers  possessing  such  instruments,  by 
enabling  them  to  find  easily  the  double  stars,  clus- 
ters, etc.,  which  are  in  a  convenient  position  for 
observation  at  any  period  of  the  year.  Those  who 
have  spent  hours  in  looking  through  books  of  astron- 
omy, in  order  to  see  what  suitable  subjects  for  their 
telescopes  are  above  the  horizon  at  any  particular 
time,  will  easily  understand  the  advantage  of  this 
arrangement. — From  DR.  CLARKE'S  "How  to  Find 
the  Stars"  

HOW  TO  TIKD  THE  STAES. 

The  object  of  this  little  book  is  to  help  the  beginner  to 
become  better  acquainted,  in  the  easiest  way,  with  the  visible 
starry  heavens ;  to  know  the  winter  and  summer  constella- 
tions, and  the  principal  fixed  stars.  It  shows  the  position  of 
the  constellations  at  different  periods  of  the  year,  giving  their 
place  in  each  of  the  four  seasons.  It  also  shows  how  to  find 
the  separate  clusters  by  a  series  of  triangles  and  diagrams, 
covering  the  whole  heavens,  and  connecting  each  constella- 
tion with  its  neighbors.  It  indicates  the  most  interesting 
objects  at  each  period  of  the  year,  especially  such  as  can  be 
found  with  a  telescope  of  moderate  power:  It  closes  with  a 
description  of  the  Astronomical  Lantern. 


f"  e  former  price  of  the  Lantern  was  $6.00 ;  we  now  offer 
It,  in  improved  form,  with  seventeen  slides  and  a  copy  oj 
"  How  TO  FIND  THE  STARS,"  for  $4.50.  The  latter  is  also 
sold  separately  at  15  cents  per  copy. 


D.  C.  HEATH  &  CO.,  Publishers, 

5   SOMERSET   STREET,   BOSTON. 


The  following  testimonials  from  those  who  have  used 
this  Lantern  have  been  recently  received:  — 

C.  A.  Young,  Prof,  of  Astronomy,  Princeton  College :  I  have 
carefully  examined  Dr.  Freeman  Clarke's  Astronomical  Lan- 
tern, and  find  it  to  be  an  admirably  contrived  apparatus  for  its 
purpose,  —  simple,  easily  managed,  and  effective.  I  think  an 
adequate  knowledge  of  the  constellations  could  be  obtained  by 
its  use,  in  connection  with  the  little  book  that  accompanies  it, 
more  rapidly  and  easily  than  from  the  most  elaborate  and  ex- 
pensive celestial  globe.  (Aug.  8,  1885.) 

C.  S.  Lyman,  Prof. of  Ast ronomy,  Yale  College:  Dr.  Clarke's 
Lantern  is  certainly  a  very  simple  and  happy  device  for  facili- 
tating the  study  of  the  stellar  configurations,  and  aiding  the 
student  in  familiarizing  himself  with  the  nightly  aspects  of  the 
heavens.  The  mere  study  of  the  constellations  is,  indeed,  but  a 
small  part  of  astronomy,  yet  a  part  both  interesting  and  important 
to  the  beginner ;  and  I  have  never  known  any  contrivance  that 
could  compare  with  this  Lantern  for  saving  alike  time,  trouble, 
and  eye-sight,  and  rendering  such  study  attractive  and  easy. 
It  is  such  a  device  as  the  writer  well  remembers  often  desiring, 
and  even  purposing  to  construct,  yet  never  brought  to  pass. 
Schools,  academies,  colleges,  and  amateur  astronomers  cannot 
fail  to  find  it  useful,  and  all  who  use  it  will  feel  thankful  to  Dr. 
Clarke  and  his  publishers  for  putting  so  convenient  a  piece  of 
apparatus  within  their  reach.  (Dec.  15,  1885.) 

0.  C.  Wendell,  Harvard  Coll.  Observatory :  I  have  examined 
the  Astronomical  Lantern,  and  find  it  well  adapted  to  its  pur- 
pose. It  combines  in  a  high  degree  simplicity  with  clearness, 
and,  for  beginners  and  amateurs,  I  think  it  has  no  equal. 
Among  its  salient  features  are  its  giving  bright  stars  on  a  dark 
field,  together  with  the  fact  that  it  represents  the  magnitudes  of 
the  stars  by  the  size  of  the  apertures.  This  is  a  great  help  to 
young  people,  from  its  naturalness.  Besides,  the  diffused  light 
transmitted  through  the  cardboard  enables  one  easily  to  see  the 
printed  magnitudes,  as  well  as  letters  and  constellations.  Mr. 
Clarke  seems  to  have  done  a  real  service  to  the  youthful  patrons 
of  astronomy  in  devising  a  lantern  which  is  at  once  portable, 
highly  entertaining,  and  so  cheap  as  to  be  within  the  reach  of 
all.  I  am  confident  that  the  names  of  the  principal  stars  and 
constellations  can  be  learned  from  it  in  half  the  time  required  to 
learn  them  from  an  ordinary  map.  (Nov.  18, 1885.) 


C.  Gtetchell,  Science  Teacher,  Phillips  Exeter  Acad. :  I  con- 
*ider  Dr.  Clarke's  Astronomical  Lantern  the  best  means  for 
enabling  students  to  identify  in  the  heavens  those  stars  which 
they  have  studied  from  a  map  or  globe.  In  the  recitation-room 
it  shows  to  the  whole  class  the  constellations  in  the  same  posi- 
tions in  which  they  appear  in  the  sky.  In  case  the  teacher 
does  not  have  the  opportunity  for  much  out-door  work,  good 
results  are  obtained  by  requiring  each  pupil  to  make  for  himself 
a  set  of  perforated  maps  from  his  own  observation.  These 
maps  may  be  verified  by  comparison  with  those  furnished  with 
the  Lantern.  (June  29,  1885.) 

E.  H.  Rudd,  Science  Teacher,  St.  Mary's  School,  Knoxville, 
III. :  I  have  used  Dr.  Clarke's  Astronomical  Lantern  for 
two  years,  and  find  it  of  the  greatest  practical  benefit  to  my 
classes  in  astronomy.  There  is  nothing  that  I  know  of  which 
could  take  its  place.  The  interesting  part  of  astronomy  to  most 
pupils  is  learning  the  names,  form,  and  location  of  constella- 
tions. My  experience  is,  that  the  Lantern,  for  this  purpose,  is 
worth  a  dozen  globes  or  charts.  Nothing,  to  my  mind,  is  better 
than  the  system  of  triangulation  as  a  help  to  location. 
(Aug.  1,  1885.) 

R.  W.  B.  Elliott,  San  Antonio,  Tex.:  I  have  found  the 
Astronomical  Lantern,  invented  by  the  Rev.  Dr.  J.  F.  Clarke, 
very  useful  in  arousing  the  interest  of  my  children,  and  enabling 
them  to  identify  the  different  stars  and  constellations.  It  fur- 
nishes a  very  pleasant  and  instructive  means  of  passing  the 
earlier  parts  of  our  bright  Texas  nights.  (July  27,  1885.) 

Mary  A.  Brackett,  Prin.  Private  School,  Brooklyn :  I  think 
it  by  far  the  best  thing  of  the  kind  I  have  ever  seen.  Any  be- 
ginner in  the  study  of  practical  astronomy  could  not  fail  to 
derive  great  pleasure  and  help  from  it.  Its  simplicity  gives  it 
its  great  charm.  {Aug.  8,  1885.) 

Clement  B.  Smyth,  New  York :  Dr.  Clarke's  Astronomical 
Lantern,  one  of  which  I  purchased  for  my  daughter,  has  been  of 
great  interest  and  aid  to  her  in  her  studies.  It  is  an  apparatus 
which,  if  known  to  those  interested  in  this  study,  would,  I 
should  think,  be  very  frequently  called  for.  My  daughter  is 
delighted  with  it,  and  feels  greatly  indebted  to  her  teachers,  the 
Misses  Brackett,  of  Brooklyn,  who  kindly  advised  her  of  its 
value,  and  where  to  procure  one.  (July  27,  1885.) 


Stye  Stellar  Jelluriar?. 

THIS  instrument  illustrates  all  the  essential  principles  of  Celestial  Me- 
chanics in  so  simple  and  clear  a  manner  that  the  pupil  can  understand  in  a  few 
hours  what  he  could  not  grasp  in  months  of  mere  book  study,  if  at  all.  It  is 
accompanied  by  a  Manual  Of  Direction  describing  nearly  a 
hundred  different  illustrations,  an  examination  of  which  cannot  but  convince 
the  teacher  of  the  wonderful  capabilities  of  the  instrument. 


The  following  are  a  few  of  many  similar 

TESTIMONIALS. 

I  am  satisfied  that  the  Stellar  Tellurian  is  the  best  instrument  of  :.ts  kind 
ever  offered  to  the  public.  Almost  every  idea  cf  Astronomy  is  made  se»  plain 
that  a  child  can  easily  understand  it.  It  should  be  in  all  schools.  —  Presi- 
dent Craven,  late  of  Trinity  College,  Hartford,  Conn. 

(0 


t  am  well  acquainted  with  the  Stellar  Tellurian,  and  consider  it  a  great 
help  in  teaching  the  elements  of  Astronomy.  I  think  it  the  best  instrument 
yet  made  for  illustrating  the  motions  of  the  earth,  and  the  phenomena  caused 
by  these  motions.  I  intend  to  use  the  instrument  at  the  college  as  soon  as  we 
have  more  room  for  apparatus.  —  J.  A.  Gillet,  Professor  of  Physics,  New 
York  Normal  College, 

I  have  examined  the  Stellar  Tellurian,  and  am  much  pleased  with  it.  I 
believe  in  appealing  to  the  eye  in  giving  instruction,  where  it  can  be  done 
without  giving  wrong  impressions.  I  think  this  is  made  on  correct  princi- 
ples. It  is  also  worthy  of  note  that  it  appears  to  be  very  durable,  and,  with 
ordinary  care,  is  not  liable  to  get  out  of  repair.  —  De  Volson  Wood,  Pro- 
fessor of  Civil  Engineering,  Stevens  Institute  (N.J.}  of  Technology. 

I  have  been  examining  to-day  the  Stellar  Tellurian,  and  am  glad  to  express 
my  opinion  of  its  value.  The  number  of  phenomena  in  Astronomy,  which  it 
beautifully  illustrates,  is  very  great,  and  the  illustration  in  each  case  is  as 
nearly  perfect  as  can  be.  The  use  of  the  Tellurian  in  the  schoolroom  must 
aid  the  pupil  in  getting  definite  conceptions,  as  well  as  awaken  new  interest 
in  Astronomy.  I  recommend  its  use  with  entire  confidence.—  Kendall 
Brooks,  President  Kalamazoo  College. 


JACKSON'S 

CELESTIAL    HEMISPHERES. 


THESE  are  two  Wall  Maps,  each  5  feet  in  diameter,  upon  which  the  pupil 
may  trace  the  constellations  as  if  he  were  pointing  them  out  in  the  sky.  With 
them  is  a  Key  in  which  are  the  Mythological  figures,  names  of  constella- 
tions, principal  stars,  etc.  Arranged  for  the  Standard  Epoch,  1880. 

By  EDWARD  P.  JACKSON,  A.M.     Author  of  "The  Earth  in 
"Space  :  A  Manual  of  Astronomical  Geography." 


D.   C.    HEATH   &  CO.,  Boston,  Mass. 
fa) 


THE  COLD  FACTS' 

of  Geography  must  be  taught;  but  the  methods 
of  presenting  them  are  made  much  more  pleasant 
and  effective  by  using  the  following  new  aids : 

Picturesque  Geography.     12  lithograph  plates, 

15  x  20  inches,  and  pamphlet  describing  their  use.    Per 

set,  $3.00 ;  mounted,  $5.00. 

Mrs.  L.  P.  Hopkins,  Supervisor  in  Boston  Schools. — "I 
have  examined  everything  I  could  find  in  this  line,  and  think 
these  altogether  the  best.  I  have  urged  very  strongly  that  a 
set  be  furnished  each  primary  school  in  the  city." 

Dr.  William  T.  Harris,  Concord,  Mass.  — "  Of  real  ser- 
vice in  teaching  the  child  the  concrete  meaning  of  the  techni- 
cal terms  used  in  Geography." 

Jackson's  Earth  in  Space.  Presents  simply  the 
main  features  of  Astronomical  Geography  for  Gram- 
mar and  Intermediate  Schools.  The  only  book  on  the 
subject.  Price  30  cents. 

"  SCHOOL  COMMITTEE  ROOMS,  BOSTON,  May  — ,  1889. 
"  Voted  unanimously,  that  fifty  Jackson's  Earth  in  Space  be  purchased 
for  each  Grammar  School." 

Redway's  Manual  of  Geography  for  Teach- 
ers, i.  Hints  to  Teachers.  2.  Modern  Facts  and  Ancient 
Fancies. 

Nichols'  Topics  in  Geography.    A  Transcript 

of  successful  work  in  the  school-room. 

Progressive  Outline  Maps,  printed  in  dim  out- 
line, to  be  filled  in  by  the  pupil,  with  the  graphic 
representation  of  all  kinds  of  geographical  facts.  Thou- 
sands of  cities  and  towns  are  using  them.  Sample  map 
and  circulars  free.  Price  by  mail,  2  cents  each  ;  $1.50 
per  hundred. 

Lucretia  R.  Crocker,  late  Supervisor  of  Schools,  Boston. — 
"I  shall  advise  the  use  of  these  'Outlines'  in  our  work." 

E.    E.  White,   recently  Supt.  of  Schools,  Cincinnati.  —  "I 
hold  map-drawing  to  be  a  means  and  not  an  end.    I  there- 
fore shall  use  and  strongly  commend  your  maps." 
Write  for  Circulars  and  Price  I/ists. 

D.  C.  HEATH  &  CO,,  Publishers, 

BOSTON.  NEW  YORK.  CHICAGO. 


GUIDES  FOR  SCIENCE-TEACHING, 


INTENDED   FOR  TEACHERS  WHO  DESIRE  TO  PRACTICALLY 
INSTRUCT  CLASSES   IN   NATURAL  HISTORY. 


I.  Hyatt's  About  Pebbles  .        .         .         .    $  .10 

II.  Goodale's  Concerning  a  Few  Common  Plants,    .15 

III.  Hyatt's  Commercial  and  Other  Sponges    .         .20 

IV.  Agassiz's  First  Lesson  in  Natural  History,       .20 
V.  Hyatt's  Corals  and  Echinoderms         .         .         .20 

VI.  Hyatt's  Mollusca 25 

VII.  Hyatt's  Worms  and  Crustacea    ...         .25 

XII.  Crosby's  Common  Minerals        '  .  .40 

XIII.  Richards'  First  Lessons  in  Minerals  .         .        .10 

IN  PREPARATION ' : 

VIII.     Hyatt's  Insects.      Grasshopper. 
IX.     Hyatt's  Fishes  and  Frogs.      Yellovv  Perch,  Common 

Frog,  and  Toad. 
X.     Hyatt's  Reptiles  and  Birds.    Alligators  and  Turtles, 

and  Pigeon. 
XI.     Hyatt's  Mammals.     Domestic  Rat. 


D.  C.  HEATH  &  CO.,  Publishers, 

BOSTON. 


